EUR RSCEUR Relative Strength Comparison to the basket of other major currencies.
eur = (eurusd + eurgbp + eurjpy/100 + eurcad + eurchf + euraud + eurnzd)/7
Recherche dans les scripts pour "deep股票代码"
AUD RSCAUD Relative Strength Comparison to the basket of other major currencies.
aud = (audusd + audjpy/100 + audcad + audchf + 1/euraud + 1/gbpaud + audnzd)/7
CHF RSCCHF Relative Strength Comparison to the basket of other major currencies.
chf = (1/usdchf + chfjpy/100 + 1/cadchf + 1/gbpchf + 1/eurchf + 1/audchf + 1/nzdchf)/7
CAD RSCCAD Relative Strength Comparison to the basket of other major currencies.
cad = (1/usdcad + cadjpy/100 + cadchf + 1/eurcad + 1/gbpcad + 1/audcad + 1/nzdcad)/7
JPY RSCJPY Relative Strength Comparison to the basket of other major currencies.
jpy = (1/usdjpy + 1/cadjpy + 1/chfjpy + 1/eurjpy + 1/gbpjpy + 1/audjpy + 1/nzdjpy)/0.07
GBP RSCGBP Relative Strength Comparison to the basket of other major currencies.
gbp = (gbpusd + gbpjpy/100 + gbpcad + 1/eurgbp + gbpchf + gbpaud + gbpnzd)/7
USD Relative Strength Comparison (RSC)Simple indicator implementing relative strength against the equally weighted basket of major currencies. Perhaps I will coin it the Equally Weighted Index (EWI) and trademark it like ICE did with DXY.
usd = (usdjpy/100 + usdcad + 1/gbpusd + 1/eurusd + usdchf + 1/audusd + 1/nzdusd)/7
DXY is hard to compare against other indices because of it's weightening. Secondly it does not compare against all majors and includes SEK which is not a major currency. Source: Wikipedia .
In this chart it becomes more clear why GU is in an uptrend. From April 25th USD has been consolidating against the basket of majors while GBP has gained in strength against the same basket.
gbp = (gbpusd + gbpjpy/100 + gbpcad + 1/eurgbp + gbpchf + gbpaud + gbpnzd)/7
Grothendieck-Teichmüller Geometric SynthesisDskyz's Grothendieck-Teichmüller Geometric Synthesis (GTGS)
THEORETICAL FOUNDATION: A SYMPHONY OF GEOMETRIES
The 🎓 GTGS is built upon a revolutionary premise: that market dynamics can be modeled as geometric and topological structures. While not a literal academic implementation—such a task would demand computational power far beyond current trading platforms—it leverages core ideas from advanced mathematical theories as powerful analogies and frameworks for its algorithms. Each component translates an abstract concept into a practical market calculation, distinguishing GTGS by identifying deeper structural patterns rather than relying on standard statistical measures.
1. Grothendieck-Teichmüller Theory: Deforming Market Structure
The Theory : Studies symmetries and deformations of geometric objects, focusing on the "absolute" structure of mathematical spaces.
Indicator Analogy : The calculate_grothendieck_field function models price action as a "deformation" from its immediate state. Using the nth root of price ratios (math.pow(price_ratio, 1.0/prime)), it measures market "shape" stretching or compression, revealing underlying tensions and potential shifts.
2. Topos Theory & Sheaf Cohomology: From Local to Global Patterns
The Theory : A framework for assembling local properties into a global picture, with cohomology measuring "obstructions" to consistency.
Indicator Analogy : The calculate_topos_coherence function uses sine waves (math.sin) to represent local price "sections." Summing these yields a "cohomology" value, quantifying price action consistency. High values indicate coherent trends; low values signal conflict and uncertainty.
3. Tropical Geometry: Simplifying Complexity
The Theory : Transforms complex multiplicative problems into simpler, additive, piecewise-linear ones using min(a, b) for addition and a + b for multiplication.
Indicator Analogy : The calculate_tropical_metric function applies tropical_add(a, b) => math.min(a, b) to identify the "lowest energy" state among recent price points, pinpointing critical support levels non-linearly.
4. Motivic Cohomology & Non-Commutative Geometry
The Theory : Studies deep arithmetic and quantum-like properties of geometric spaces.
Indicator Analogy : The motivic_rank and spectral_triple functions compute weighted sums of historical prices to capture market "arithmetic complexity" and "spectral signature." Higher values reflect structured, harmonic price movements.
5. Perfectoid Spaces & Homotopy Type Theory
The Theory : Abstract fields dealing with p-adic numbers and logical foundations of mathematics.
Indicator Analogy : The perfectoid_conv and type_coherence functions analyze price convergence and path identity, assessing the "fractal dust" of price differences and price path cohesion, adding fractal and logical analysis.
The Combination is Key : No single theory dominates. GTGS ’s Unified Field synthesizes all seven perspectives into a comprehensive score, ensuring signals reflect deep structural alignment across mathematical domains.
🎛️ INPUTS: CONFIGURING THE GEOMETRIC ENGINE
The GTGS offers a suite of customizable inputs, allowing traders to tailor its behavior to specific timeframes, market sectors, and trading styles. Below is a detailed breakdown of key input groups, their functionality, and optimization strategies, leveraging provided tooltips for precision.
Grothendieck-Teichmüller Theory Inputs
🧬 Deformation Depth (Absolute Galois) :
What It Is : Controls the depth of Galois group deformations analyzed in market structure.
How It Works : Measures price action deformations under automorphisms of the absolute Galois group, capturing market symmetries.
Optimization :
Higher Values (15-20) : Captures deeper symmetries, ideal for major trends in swing trading (4H-1D).
Lower Values (3-8) : Responsive to local deformations, suited for scalping (1-5min).
Timeframes :
Scalping (1-5min) : 3-6 for quick local shifts.
Day Trading (15min-1H) : 8-12 for balanced analysis.
Swing Trading (4H-1D) : 12-20 for deep structural trends.
Sectors :
Stocks : Use 8-12 for stable trends.
Crypto : 3-8 for volatile, short-term moves.
Forex : 12-15 for smooth, cyclical patterns.
Pro Tip : Increase in trending markets to filter noise; decrease in choppy markets for sensitivity.
🗼 Teichmüller Tower Height :
What It Is : Determines the height of the Teichmüller modular tower for hierarchical pattern detection.
How It Works : Builds modular levels to identify nested market patterns.
Optimization :
Higher Values (6-8) : Detects complex fractals, ideal for swing trading.
Lower Values (2-4) : Focuses on primary patterns, faster for scalping.
Timeframes :
Scalping : 2-3 for speed.
Day Trading : 4-5 for balanced patterns.
Swing Trading : 5-8 for deep fractals.
Sectors :
Indices : 5-8 for robust, long-term patterns.
Crypto : 2-4 for rapid shifts.
Commodities : 4-6 for cyclical trends.
Pro Tip : Higher towers reveal hidden fractals but may slow computation; adjust based on hardware.
🔢 Galois Prime Base :
What It Is : Sets the prime base for Galois field computations.
How It Works : Defines the field extension characteristic for market analysis.
Optimization :
Prime Characteristics :
2 : Binary markets (up/down).
3 : Ternary states (bull/bear/neutral).
5 : Pentagonal symmetry (Elliott waves).
7 : Heptagonal cycles (weekly patterns).
11,13,17,19 : Higher-order patterns.
Timeframes :
Scalping/Day Trading : 2 or 3 for simplicity.
Swing Trading : 5 or 7 for wave or cycle detection.
Sectors :
Forex : 5 for Elliott wave alignment.
Stocks : 7 for weekly cycle consistency.
Crypto : 3 for volatile state shifts.
Pro Tip : Use 7 for most markets; 5 for Elliott wave traders.
Topos Theory & Sheaf Cohomology Inputs
🏛️ Temporal Site Size :
What It Is : Defines the number of time points in the topological site.
How It Works : Sets the local neighborhood for sheaf computations, affecting cohomology smoothness.
Optimization :
Higher Values (30-50) : Smoother cohomology, better for trends in swing trading.
Lower Values (5-15) : Responsive, ideal for reversals in scalping.
Timeframes :
Scalping : 5-10 for quick responses.
Day Trading : 15-25 for balanced analysis.
Swing Trading : 25-50 for smooth trends.
Sectors :
Stocks : 25-35 for stable trends.
Crypto : 5-15 for volatility.
Forex : 20-30 for smooth cycles.
Pro Tip : Match site size to your average holding period in bars for optimal coherence.
📐 Sheaf Cohomology Degree :
What It Is : Sets the maximum degree of cohomology groups computed.
How It Works : Higher degrees capture complex topological obstructions.
Optimization :
Degree Meanings :
1 : Simple obstructions (basic support/resistance).
2 : Cohomological pairs (double tops/bottoms).
3 : Triple intersections (complex patterns).
4-5 : Higher-order structures (rare events).
Timeframes :
Scalping/Day Trading : 1-2 for simplicity.
Swing Trading : 3 for complex patterns.
Sectors :
Indices : 2-3 for robust patterns.
Crypto : 1-2 for rapid shifts.
Commodities : 3-4 for cyclical events.
Pro Tip : Degree 3 is optimal for most trading; higher degrees for research or rare event detection.
🌐 Grothendieck Topology :
What It Is : Chooses the Grothendieck topology for the site.
How It Works : Affects how local data integrates into global patterns.
Optimization :
Topology Characteristics :
Étale : Finest topology, captures local-global principles.
Nisnevich : A1-invariant, good for trends.
Zariski : Coarse but robust, filters noise.
Fpqc : Faithfully flat, highly sensitive.
Sectors :
Stocks : Zariski for stability.
Crypto : Étale for sensitivity.
Forex : Nisnevich for smooth trends.
Indices : Zariski for robustness.
Timeframes :
Scalping : Étale for precision.
Swing Trading : Nisnevich or Zariski for reliability.
Pro Tip : Start with Étale for precision; switch to Zariski in noisy markets.
Unified Field Configuration Inputs
⚛️ Field Coupling Constant :
What It Is : Sets the interaction strength between geometric components.
How It Works : Controls signal amplification in the unified field equation.
Optimization :
Higher Values (0.5-1.0) : Strong coupling, amplified signals for ranging markets.
Lower Values (0.001-0.1) : Subtle signals for trending markets.
Timeframes :
Scalping : 0.5-0.8 for quick, strong signals.
Swing Trading : 0.1-0.3 for trend confirmation.
Sectors :
Crypto : 0.5-1.0 for volatility.
Stocks : 0.1-0.3 for stability.
Forex : 0.3-0.5 for balance.
Pro Tip : Default 0.137 (fine structure constant) is a balanced starting point; adjust up in choppy markets.
📐 Geometric Weighting Scheme :
What It Is : Determines the framework for combining geometric components.
How It Works : Adjusts emphasis on different mathematical structures.
Optimization :
Scheme Characteristics :
Canonical : Equal weighting, balanced.
Derived : Emphasizes higher-order structures.
Motivic : Prioritizes arithmetic properties.
Spectral : Focuses on frequency domain.
Sectors :
Stocks : Canonical for balance.
Crypto : Spectral for volatility.
Forex : Derived for structured moves.
Indices : Motivic for arithmetic cycles.
Timeframes :
Day Trading : Canonical or Derived for flexibility.
Swing Trading : Motivic for long-term cycles.
Pro Tip : Start with Canonical; experiment with Spectral in volatile markets.
Dashboard and Visual Configuration Inputs
📋 Show Enhanced Dashboard, 📏 Size, 📍 Position :
What They Are : Control dashboard visibility, size, and placement.
How They Work : Display key metrics like Unified Field , Resonance , and Signal Quality .
Optimization :
Scalping : Small size, Bottom Right for minimal chart obstruction.
Swing Trading : Large size, Top Right for detailed analysis.
Sectors : Universal across markets; adjust size based on screen setup.
Pro Tip : Use Large for analysis, Small for live trading.
📐 Show Motivic Cohomology Bands, 🌊 Morphism Flow, 🔮 Future Projection, 🔷 Holographic Mesh, ⚛️ Spectral Flow :
What They Are : Toggle visual elements representing mathematical calculations.
How They Work : Provide intuitive representations of market dynamics.
Optimization :
Timeframes :
Scalping : Enable Morphism Flow and Spectral Flow for momentum.
Swing Trading : Enable all for comprehensive analysis.
Sectors :
Crypto : Emphasize Morphism Flow and Future Projection for volatility.
Stocks : Focus on Cohomology Bands for stable trends.
Pro Tip : Disable non-essential visuals in fast markets to reduce clutter.
🌫️ Field Transparency, 🔄 Web Recursion Depth, 🎨 Mesh Color Scheme :
What They Are : Adjust visual clarity, complexity, and color.
How They Work : Enhance interpretability of visual elements.
Optimization :
Transparency : 30-50 for balanced visibility; lower for analysis.
Recursion Depth : 6-8 for balanced detail; lower for older hardware.
Color Scheme :
Purple/Blue : Analytical focus.
Green/Orange : Trading momentum.
Pro Tip : Use Neon Purple for deep analysis; Neon Green for active trading.
⏱️ Minimum Bars Between Signals :
What It Is : Minimum number of bars required between consecutive signals.
How It Works : Prevents signal clustering by enforcing a cooldown period.
Optimization :
Higher Values (10-20) : Fewer signals, avoids whipsaws, suited for swing trading.
Lower Values (0-5) : More responsive, allows quick reversals, ideal for scalping.
Timeframes :
Scalping : 0-2 bars for rapid signals.
Day Trading : 3-5 bars for balance.
Swing Trading : 5-10 bars for stability.
Sectors :
Crypto : 0-3 for volatility.
Stocks : 5-10 for trend clarity.
Forex : 3-7 for cyclical moves.
Pro Tip : Increase in choppy markets to filter noise.
Hardcoded Parameters
Tropical, Motivic, Spectral, Perfectoid, Homotopy Inputs : Fixed to optimize performance but influence calculations (e.g., tropical_degree=4 for support levels, perfectoid_prime=5 for convergence).
Optimization : Experiment with codebase modifications if advanced customization is needed, but defaults are robust across markets.
🎨 ADVANCED VISUAL SYSTEM: TRADING IN A GEOMETRIC UNIVERSE
The GTTMTSF ’s visuals are direct representations of its mathematics, designed for intuitive and precise trading decisions.
Motivic Cohomology Bands :
What They Are : Dynamic bands ( H⁰ , H¹ , H² ) representing cohomological support/resistance.
Color & Meaning : Colors reflect energy levels ( H⁰ tightest, H² widest). Breaks into H¹ signal momentum; H² touches suggest reversals.
How to Trade : Use for stop-loss/profit-taking. Band bounces with Dashboard confirmation are high-probability setups.
Morphism Flow (Webbing) :
What It Is : White particle streams visualizing market momentum.
Interpretation : Dense flows indicate strong trends; sparse flows signal consolidation.
How to Trade : Follow dominant flow direction; new flows post-consolidation signal trend starts.
Future Projection Web (Fractal Grid) :
What It Is : Fibonacci-period fractal projections of support/resistance.
Color & Meaning : Three-layer lines (white shadow, glow, colored quantum) with labels showing price, topological class, anomaly strength (φ), resonance (ρ), and obstruction ( H¹ ). ⚡ marks extreme anomalies.
How to Trade : Target ⚡/● levels for entries/exits. High-anomaly levels with weakening Unified Field are reversal setups.
Holographic Mesh & Spectral Flow :
What They Are : Visuals of harmonic interference and spectral energy.
How to Trade : Bright mesh nodes or strong Spectral Flow warn of building pressure before price movement.
📊 THE GEOMETRIC DASHBOARD: YOUR MISSION CONTROL
The Dashboard translates complex mathematics into actionable intelligence.
Unified Field & Signals :
FIELD : Master value (-10 to +10), synthesizing all geometric components. Extreme readings (>5 or <-5) signal structural limits, often preceding reversals or continuations.
RESONANCE : Measures harmony between geometric field and price-volume momentum. Positive amplifies bullish moves; negative amplifies bearish moves.
SIGNAL QUALITY : Confidence meter rating alignment. Trade only STRONG or EXCEPTIONAL signals for high-probability setups.
Geometric Components :
What They Are : Breakdown of seven mathematical engines.
How to Use : Watch for convergence. A strong Unified Field is reliable when components (e.g., Grothendieck , Topos , Motivic ) align. Divergence warns of trend weakening.
Signal Performance :
What It Is : Tracks indicator signal performance.
How to Use : Assesses real-time performance to build confidence and understand system behavior.
🚀 DEVELOPMENT & UNIQUENESS: BEYOND CONVENTIONAL ANALYSIS
The GTTMTSF was developed to analyze markets as evolving geometric objects, not statistical time-series.
Why This Is Unlike Anything Else :
Theoretical Depth : Uses geometry and topology, identifying patterns invisible to statistical tools.
Holistic Synthesis : Integrates seven deep mathematical frameworks into a cohesive Unified Field .
Creative Implementation : Translates PhD-level mathematics into functional Pine Script , blending theory and practice.
Immersive Visualization : Transforms charts into dynamic geometric landscapes for intuitive market understanding.
The GTTMTSF is more than an indicator; it’s a new lens for viewing markets, for traders seeking deeper insight into hidden order within chaos.
" Where there is matter, there is geometry. " - Johannes Kepler
— Dskyz , Trade with insight. Trade with anticipation.
RSI of RSI Deviation (RoRD)RSI of RSI Deviation (RoRD) - Advanced Momentum Acceleration Analysis
What is RSI of RSI Deviation (RoRD)?
RSI of RSI Deviation (RoRD) is a insightful momentum indicator that transcends traditional oscillator analysis by measuring the acceleration of momentum through sophisticated mathematical layering. By calculating RSI on RSI itself (RSI²) and applying advanced statistical deviation analysis with T3 smoothing, RoRD reveals hidden market dynamics that single-layer indicators miss entirely.
This isn't just another RSI variant—it's a complete reimagining of how we measure and visualize momentum dynamics. Where traditional RSI shows momentum, RoRD shows momentum's rate of change . Where others show static overbought/oversold levels, RoRD reveals statistically significant deviations unique to each market's character.
Theoretical Foundation - The Mathematics of Momentum Acceleration
1. RSI² (RSI of RSI) - The Core Innovation
Traditional RSI measures price momentum. RoRD goes deeper:
Primary RSI (RSI₁) : Standard RSI calculation on price
Secondary RSI (RSI²) : RSI calculated on RSI₁ values
This creates a "momentum of momentum" indicator that leads price action
Mathematical Expression:
RSI₁ = 100 - (100 / (1 + RS₁))
RSI² = 100 - (100 / (1 + RS₂))
Where RS₂ = Average Gain of RSI₁ / Average Loss of RSI₁
2. T3 Smoothing - Lag-Free Response
The T3 Moving Average, developed by Tim Tillson, provides:
Superior smoothing with minimal lag
Adaptive response through volume factor (vFactor)
Noise reduction while preserving signal integrity
T3 Formula:
T3 = c1×e6 + c2×e5 + c3×e4 + c4×e3
Where e1...e6 are cascaded EMAs and c1...c4 are volume-factor-based coefficients
3. Statistical Z-Score Deviation
RoRD employs dual-layer Z-score normalization :
Initial Z-Score : (RSI² - SMA) / StDev
Final Z-Score : Z-score of the Z-score for refined extremity detection
This identifies statistically rare events relative to recent market behavior
4. Multi-Timeframe Confluence
Compares current timeframe Z-score with higher timeframe (HTF)
Provides directional confirmation across time horizons
Filters false signals through timeframe alignment
Why RoRD is Different & More Sophisticated
Beyond Traditional Indicators:
Acceleration vs. Velocity : While RSI measures momentum (velocity), RoRD measures momentum's rate of change (acceleration)
Adaptive Thresholds : Z-score analysis adapts to market conditions rather than using fixed 70/30 levels
Statistical Significance : Signals are based on mathematical rarity, not arbitrary levels
Leading Indicator : RSI² often turns before price, providing earlier signals
Reduced Whipsaws : T3 smoothing eliminates noise while maintaining responsiveness
Unique Signal Generation:
Quantum Orbs : Multi-layered visual signals for statistically extreme events
Divergence Detection : Automated identification of price/momentum divergences
Regime Backgrounds : Visual market state classification (Bullish/Bearish/Neutral)
Particle Effects : Dynamic visualization of momentum energy
Visual Design & Interpretation Guide
Color Coding System:
Yellow (#e1ff00) : Neutral/balanced momentum state
Red (#ff0000) : Overbought/extreme bullish acceleration
Green (#2fff00) : Oversold/extreme bearish acceleration
Orange : Z-score visualization
Blue : HTF Z-score comparison
Main Visual Elements:
RSI² Line with Glow Effect
Multi-layer glow creates depth and emphasis
Color dynamically shifts based on momentum state
Line thickness indicates signal strength
Quantum Signal Orbs
Green Orbs Below : Statistically rare oversold conditions
Red Orbs Above : Statistically rare overbought conditions
Multiple layers indicate signal strength
Only appear at Z-score extremes for high-conviction signals
Divergence Markers
Green Circles : Bullish divergence detected
Red Circles : Bearish divergence detected
Plotted at pivot points for precision
Background Regimes
Green Background : Bullish momentum regime
Grey Background : Bearish momentum regime
Blue Background : Neutral/transitioning regime
Particle Effects
Density indicates momentum energy
Color matches current RSI² state
Provides dynamic market "feel"
Dashboard Metrics - Deep Dive
RSI² ANALYSIS Section:
RSI² Value (0-100)
Current smoothed RSI of RSI reading
>70 : Strong bullish acceleration
<30 : Strong bearish acceleration
~50 : Neutral momentum state
RSI¹ Value
Traditional RSI for reference
Compare with RSI² for acceleration/deceleration insights
Z-Score Status
🔥 EXTREME HIGH : Z > threshold, statistically rare bullish
❄️ EXTREME LOW : Z < threshold, statistically rare bearish
📈 HIGH/📉 LOW : Elevated but not extreme
➡️ NEUTRAL : Normal statistical range
MOMENTUM Section:
Velocity Indicator
▲▲▲ : Strong positive acceleration
▼▼▼ : Strong negative acceleration
Shows rate of change in RSI²
Strength Bar
██████░░░░ : Visual power gauge
Filled bars indicate momentum strength
Based on deviation from center line
SIGNALS Section:
Divergence Status
🟢 BULLISH DIV : Price making lows, RSI² making highs
🔴 BEARISH DIV : Price making highs, RSI² making lows
⚪ NO DIVERGENCE : No divergence detected
HTF Comparison
🔥 HTF EXTREME : Higher timeframe confirms extremity
📊 HTF NORMAL : Higher timeframe is neutral
Critical for multi-timeframe confirmation
Trading Application & Strategy
Signal Hierarchy (Highest to Lowest Priority):
Quantum Orb + HTF Alignment + Divergence
Highest conviction reversal signal
Z-score extreme + timeframe confluence + divergence
Quantum Orb + HTF Alignment
Strong reversal signal
Wait for price confirmation
Divergence + Regime Change
Medium-term reversal signal
Monitor for orb confirmation
Threshold Crosses
Traditional overbought/oversold
Use as alert, not entry
Entry Strategies:
For Reversals:
Wait for Quantum Orb signal
Confirm with HTF Z-score direction
Enter on price structure break
Stop beyond recent extreme
For Continuations:
Trade with regime background color
Use RSI² pullbacks to center line
Avoid signals against HTF trend
For Scalping:
Focus on Z-score extremes
Quick entries on orb signals
Exit at center line cross
Risk Management:
Reduce position size when signals conflict with HTF
Avoid trades during regime transitions (blue background)
Tighten stops after divergence completion
Scale out at statistical mean reversion
Development & Uniqueness
RoRD represents months of research into momentum dynamics and statistical analysis. Unlike indicators that simply combine existing tools, RoRD introduces several genuine innovations :
True RSI² Implementation : Not a smoothed RSI, but actual RSI calculated on RSI values
Dual Z-Score Normalization : Unique approach to finding statistical extremes
T3 Integration : First RSI² implementation with T3 smoothing for optimal lag reduction
Quantum Orb Visualization : Revolutionary signal display method
Dynamic Regime Detection : Automatic market state classification
Statistical Adaptability : Thresholds adapt to market volatility
This indicator was built from first principles, with each component carefully selected for its mathematical properties and practical trading utility. The result is a professional-grade tool that provides insights unavailable through traditional momentum analysis.
Best Practices & Tips
Start with default settings - they're optimized for most markets
Always check HTF alignment before taking signals
Use divergences as early warning , orbs as confirmation
Respect regime backgrounds - trade with them, not against
Combine with price action - RoRD shows when, price shows where
Adjust Z-score thresholds based on market volatility
Monitor dashboard metrics for complete market context
Conclusion
RoRD isn't just another indicator—it's a complete momentum analysis system that reveals market dynamics invisible to traditional tools. By combining momentum acceleration, statistical analysis, and multi-timeframe confluence with intuitive visualization, RoRD provides traders with a sophisticated edge in any market condition.
Whether you're scalping rapid reversals or positioning for major trend changes, RoRD's unique approach to momentum analysis will transform how you see and trade market dynamics.
See momentum's future. Trade with statistical edge.
Trade with insight. Trade with anticipation.
— Dskyz, for DAFE Trading Systems
Sentiment OscillatorIn the complex world of trading, understanding market sentiment can be like reading the emotional pulse of financial markets. Our Sentiment Oscillator is designed to be your personal market mood translator, helping you navigate through the noise of price movements and market fluctuations.
Imagine having a sophisticated tool that goes beyond traditional price charts, diving deep into the underlying dynamics of market behavior. This indicator doesn't just show you numbers – it tells you a story about market sentiment, combining multiple financial signals to give you a comprehensive view of potential market directions.
The Sentiment Oscillator acts like a sophisticated emotional barometer for stocks, cryptocurrencies, or any tradable asset. It analyzes price changes, market volatility, trading volume, and long-term trends to generate a unique sentiment score. This score ranges from highly bullish to deeply bearish, providing traders with an intuitive visual representation of market mood.
Green zones indicate positive market sentiment, suggesting potential buying opportunities. Red zones signal caution, hinting at possible downward trends. The oscillator's gray neutral zone helps you identify periods of market uncertainty, allowing for more calculated trading decisions.
What sets this indicator apart is its ability to blend multiple market factors into a single, easy-to-understand indicator. It's not just about current price – it's about understanding the deeper currents moving beneath the surface of market prices.
Traders can use this oscillator to:
- Identify potential trend reversals
- Understand market sentiment beyond price movement
- Spot periods of market strength or weakness
- Complement other technical analysis tools
Whether you're a day trader, swing trader, or long-term investor, the Sentiment Oscillator provides an additional layer of insight to support your trading strategy. Remember, no indicator is a crystal ball, but this tool can help you make more informed decisions in the dynamic world of trading.
Pasrsifal.RegressionTrendStateSummary
The Parsifal.Regression.Trend.State Indicator analyzes the leading coefficients of linear and quadratic regressions of price (against time). It also considers their first- and second-order changes. These features are aggregated into a Trend-State background, shown as a gradient color. In addition, the indicator generates fast and slow signals that can be used as potential entry- or exit triggers.
This tool is designed for advanced trend-following strategies, leveraging information from multiple trendline features.
Background
Trendlines provide insight into the state of a trend or the “trendiness” of a price process. While moving averages or pivot-based lines can serve as envelopes and breakout levels, they are often too lagging for swing traders, who need tools that adapt more closely to price swings, ideally using trendlines, around which the price process swings continuously.
Regression lines address this by cutting directly through the data, making them a natural anchor for observing how price winds around a central trendline within a chosen lookback period.
Regression Trendlines
• Linear Regression:
o Minimizes distance to all closing values over the lookback period.
o The slope represents the short-term linear trend.
o The change of slope indicates trend acceleration or deceleration.
o Linear regression lags during phases of rapid market shifts.
• Quadratic Regression:
o Fits a second-degree polynomial to minimize deviation from closing prices.
o The convexity term (leading coefficient) reflects curvature:
Positive convexity → accelerating uptrend or fading downtrend.
Negative convexity → accelerating downtrend or fading uptrend.
o The change of convexity detects early shifts in momentum and often reacts faster than slope features.
Features Extracted
The indicator evaluates six features:
• Linear features: slope, first derivative of slope, second derivative of slope.
• Quadratic features: convexity term, first derivative of the convexity term, second derivative of the convexity term.
• Linear features: capture broad, background trend behavior.
• Quadratic features: detect deviations, accelerations, and smaller-scale dynamics.
Quadratic terms generally react first to market changes, while linear terms provide stability and context.
Dynamics of Market Moves as seen by linear and quadratic regressions
• At the start of a rapid move:
The change of convexity reacts first, capturing the shift in dynamics before other features. The convexity term then follows, while linear slope features lag further behind. Because convexity measures deviation from linearity, it reflects accelerating momentum more effectively than slope.
• At the end of a rapid move:
Again, the change of convexity responds first to fading momentum, signaling the transition from above-linear to below-linear dynamics. Even while a strong trend persists, the change of convexity may flip sign early, offering a warning of weakening strength. The convexity term itself adjusts more slowly but may still turn before the price process does. Linear features lag the most, typically only flipping after price has already reversed, thereby smoothing out the rapid, more sensitive reactions of quadratic terms.
________________________________________
Parsifal Regression.Trend.State Method
1. Feature Mapping:
Each feature is mapped to a range between -1 and 1, preserving zero-crossings (critical for sign interpretation).
2. Aggregation:
A heuristic linear combination*) produces a background information value, visualized as a gradient color scale:
o Deep green → strong positive trend.
o Deep red → strong negative trend.
o Yellow → neutral or transitional states.
3. Signals:
o Fast signal (oscillator): ranges from -1 to 1, reflecting short-term trend state.
o Slow signal (smoothed): moving average of the fast signal.
o Their interactions (crossovers, zero-crossings) provide actionable trading triggers.
How to Use
The Trend-State background gradient provides intuitive visual feedback on the aggregated regression features (slope, convexity, and their changes). Because these features reflect not only current trend strength but also their acceleration or deceleration, the color transitions help anticipate evolving market states:
• Solid Green: All features near their highs. Indicates a strong, accelerating uptrend. May also reflect explosive or hyperbolic upside moves (including gaps).
• Fading Solid Green: A recently strong uptrend is losing momentum. Price may shift into a slower uptrend, consolidation, or even a reversal.
• Fading Green → Yellow: Often appears as a dirty yellow or a rapidly mixing pattern of green and red. Signals that the uptrend is weakening toward neutrality or beginning to turn negative.
• Yellow → Deepening Red: Two possible scenarios:
o Coming from a strong uptrend → suggests a sharp fade, though the trend may still technically be up.
o Coming from a weaker uptrend or sideways market → suggests the start of an accelerating downtrend.
• Solid Red: All features near their lows. Indicates a strong, accelerating downtrend. May also reflect crash-type conditions or downside gaps.
• Fading Solid Red: A recently strong downtrend is losing strength. Market may move into a slower decline, consolidation, or early reversal upward.
• Fading Red → Yellow : The downtrend is weakening toward neutral, with potential for a bullish shift.
• Yellow → Increasing Green: Two possible scenarios:
o Coming from a strong downtrend, it reflects a sharp fade of bearish momentum, though the market may still technically be trending down.
o Coming from a weaker downtrend or sideways movement, it suggests the start of an accelerating uptrend.
Note: Market evolution does not always follow this neat “color cycle.” It may jump between states, skip stages, or reverse abruptly depending on market conditions. This makes the background coloring particularly valuable as a contextual map of current and evolving price dynamics.
Signal Crossovers:
Although the fast signal is very similar (but not identical) to the background coloring, it provides a numerical representation indicating a bullish interpretation for rising values and bearish for falling.
o High-confidence entries:
Fast signal rising from < -0.7 and crossing above the slow signal → potential long entry.
Fast signal falling from > +0.7 and crossing below the slow signal → potential short entry.
o Low-confidence entries:
Crossovers near zero may still provide a valid trigger but may be noisy and should be confirmed with other signals.
o Zero-crossings:
Indicate broader state changes, useful for conservative positioning or option strategies. For confirmation of a Fast signal 0-crossing, wait for the Slow signal to cross as well.
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*) Note on Aggregation
While the indicator currently uses a heuristic linear combination of features, alternatives such as Principal Component Analysis (PCA) could provide a more formal aggregation. However, while in the absence of matrix algebra, the required eigenvalue decomposition can be approximated, its computational expense does not justify the marginal higher insight in this case. The current heuristic approach offers a practical balance of clarity, speed, and accuracy.
Meta-LR ForecastThis indicator builds a forward-looking projection from the current bar by combining twelve time-compressed “mini forecasts.” Each forecast is a linear-regression-based outlook whose contribution is adaptively scaled by trend strength (via ADX) and normalized to each timeframe’s own volatility (via that timeframe’s ATR). The result is a 12-segment polyline that starts at the current price and extends one bar at a time into the future (1× through 12× the chart’s timeframe). Alongside the plotted path, the script computes two summary measures:
* Per-TF Bias% — a directional efficiency × R² score for each micro-forecast, expressed as a percent.
* Meta Bias% — the same score, but applied to the final, accumulated 12-step path. It summarizes how coherent and directional the combined projection is.
This tool is an indicator, not a strategy. It does not place orders. Nothing here is trade advice; it is a visual, quantitative framework to help you assess directional bias and trend context across a ladder of timeframe multiples.
The core engine fits a simple least-squares line on a normalized price series for each small forecast horizon and extrapolates one bar forward. That “trend” forecast is paired with its mirror, an “anti-trend” forecast, constructed around the current normalized price. The model then blends between these two wings according to current trend strength as measured by ADX.
ADX is transformed into a weight (w) in using an adaptive band centered on the rolling mean (μ) with width derived from the standard deviation (σ) of ADX over a configurable lookback. When ADX is deeply below the lower band, the weight approaches -1, favoring anti-trend behavior. Inside the flat band, the weight is near zero, producing neutral behavior. Clearly above the upper band, the weight approaches +1, favoring a trend-following stance. The transitions between these regions are linear so the regime shift is smooth rather than abrupt.
You can shape how quickly the model commits to either wing using two exponents. One exponent controls how aggressively positive weights lean into the trend forecast; the other controls how aggressively negative weights lean into the anti-trend forecast. Raising these exponents makes the response more gradual; lowering them makes the shift more decisive. An optional switch can force full anti-trend behavior when ADX registers a deep-low condition far below the lower tail, if you prefer a categorical stance in very flat markets.
A key design choice is volatility normalization. Every micro-forecast is computed in ATR units of its own timeframe. The script fetches that timeframe’s ATR inside each security call and converts normalized outputs back to price with that exact ATR. This avoids scaling higher-timeframe effects by the chart ATR or by square-root time approximations. Using “ATR-true” for each timeframe keeps the cross-timeframe accumulation consistent and dimensionally correct.
Bias% is defined as directional efficiency multiplied by R², expressed as a percent. Directional efficiency captures how much net progress occurred relative to the total path length; R² captures how well the path aligns with a straight line. If price meanders without net progress, efficiency drops; if the variation is well-explained by a line, R² rises. Multiplying the two penalizes choppy, low-signal paths and rewards sustained, coherent motion.
The forward path is built by converting each per-timeframe Bias% into a small ATR-sized delta, then cumulatively adding those deltas to form a 12-step projection. This produces a polyline anchored at the current close and stepping forward one bar per timeframe multiple. Segment color flips by slope, allowing a quick read of the path’s direction and inflection.
Inputs you can tune include:
* Max Regression Length. Upper bound for each micro-forecast’s regression window. Larger values smooth the trend estimate at the cost of responsiveness; smaller values react faster but can add noise.
* Price Source. The price series analyzed (for example, close or typical price).
* ADX Length. Period used for the DMI/ADX calculation.
* ATR Length (normalization). Window used for ATR; this is applied per timeframe inside each security call.
* Band Lookback (for μ, σ). Lookback used to compute the adaptive ADX band statistics. Larger values stabilize the band; smaller values react more quickly.
* Flat half-width (σ). Width of the neutral band on both sides of μ. Wider flats spend more time neutral; narrower flats switch regimes more readily.
* Tail width beyond flat (σ). Distance from the flat band edge to the extreme trend/anti-trend zone. Larger tails create a longer ramp; smaller tails reach extremes sooner.
* Polyline Width. Visual thickness of the plotted segments.
* Negative Wing Aggression (anti-trend). Exponent shaping for negative weights; higher values soften the tilt into mean reversion.
* Positive Wing Aggression (trend). Exponent shaping for positive weights; lower values make trend commitment stronger and sooner.
* Force FULL Anti-Trend at Deep-Low ADX. Optional hard switch for extremely low ADX conditions.
On the chart you will see:
* A 12-segment forward polyline starting from the current close to bar\_index + 1 … +12, with green segments for up-steps and red for down-steps.
* A small label at the latest bar showing Meta Bias% when available, or “n/a” when insufficient data exists.
Interpreting the readouts:
* Trend-following contexts are characterized by ADX above the adaptive upper band, pushing w toward +1. The blended forecast leans toward the regression extrapolation. A strongly positive Meta Bias% in this environment suggests directional alignment across the ladder of timeframes.
* Mean-reversion contexts occur when ADX is well below the lower tail, pushing w toward -1 (or forcing anti-trend if enabled). After a sharp advance, a negative Meta Bias% may indicate the model projects pullback tendencies.
* Neutral contexts occur when ADX sits inside the flat band; w is near zero, the blended forecast remains close to current price, and Meta Bias% tends to hover near zero.
These are analytical cues, not rules. Always corroborate with your broader process, including market structure, time-of-day behavior, liquidity conditions, and risk limits.
Practical usage patterns include:
* Momentum confirmation. Combine a rising Meta Bias% with higher-timeframe structure (such as higher highs and higher lows) to validate continuation setups. Treat the 12th step’s distance as a coarse sense of potential room rather than as a target.
* Fade filtering. If you prefer fading extremes, require ADX to be near or below the lower ramp before acting on counter-moves, and avoid fades when ADX is decisively above the upper band.
* Position planning. Because per-step deltas are ATR-scaled, the path’s vertical extent can be mentally mapped to typical noise for the instrument, informing stop distance choices. The script itself does not compute orders or size.
* Multi-timeframe alignment. Each step corresponds to a clean multiple of your chart timeframe, so the polyline visualizes how successively larger windows bias price, all referenced to the current bar.
House-rules and repainting disclosures:
* Indicator, not strategy. The script does not execute, manage, or suggest orders. It displays computed paths and bias scores for analysis only.
* No performance claims. Past behavior of any measure, including Meta Bias%, does not guarantee future results. There are no assurances of profitability.
* Higher-timeframe updates. Values obtained via security for higher-timeframe series can update intrabar until the higher-timeframe bar closes. The forward path and Meta Bias% may change during formation of a higher-timeframe candle. If you need confirmed higher-timeframe inputs, consider reading the prior higher-timeframe value or acting only after the higher-timeframe close.
* Data sufficiency. The model requires enough history to compute ATR, ADX statistics, and regression windows. On very young charts or illiquid symbols, parts of the readout can be unavailable until sufficient data accumulates.
* Volatility regimes. ATR normalization helps compare across timeframes, but unusual volatility regimes can make the path look deceptively flat or exaggerated. Judge the vertical scale relative to your instrument’s typical ATR.
Tuning tips:
* Stability versus responsiveness. Increase Max Regression Length to steady the micro-forecasts but accept slower response. If you lower it, consider slightly increasing Band Lookback so regime boundaries are not too jumpy.
* Regime bands. Widen the flat half-width to spend more time neutral, which can reduce over-trading tendencies in chop. Shrink the tail width if you want the model to commit to extremes sooner, at the cost of more false swings.
* Wing shaping. If anti-trend behavior feels too abrupt at low ADX, raise the negative wing exponent. If you want trend bias to kick in more decisively at high ADX, lower the positive wing exponent. Small changes have large effects.
* Forced anti-trend. Enable the deep-low option only if you explicitly want a categorical “markets are flat, fade moves” policy. Many users prefer leaving it off to keep regime decisions continuous.
Troubleshooting:
* Nothing plots or the label shows “n/a.” Ensure the chart has enough history for the ADX band statistics, ATR, and the regression windows. Exotic or illiquid symbols with missing data may starve the higher-timeframe computations. Try a more liquid market or a higher timeframe.
* Path flickers or shifts during the bar. This is expected when any higher-timeframe input is still forming. Wait for the higher-timeframe close for fully confirmed behavior, or modify the code to read prior values from the higher timeframe.
* Polyline looks too flat or too steep. Check the chart’s vertical scale and recent ATR regime. Adjust Max Regression Length, the wing exponents, or the band widths to suit the instrument.
Integration ideas for manual workflows:
* Confluence checklist. Use Meta Bias% as one of several independent checks, alongside structure, session context, and event risk. Act only when multiple cues align.
* Stop and target thinking. Because deltas are ATR-scaled at each timeframe, benchmark your proposed stops and targets against the forward steps’ magnitude. Stops that are much tighter than the prevailing ATR often sit inside normal noise.
* Session context. Consider session hours and microstructure. The same ADX value can imply different tradeability in different sessions, particularly in index futures and FX.
This indicator deliberately avoids:
* Fixed thresholds for buy or sell decisions. Markets vary and fixed numbers invite overfitting. Decide what constitutes “high enough” Meta Bias% for your market and timeframe.
* Automatic risk sizing. Proper sizing depends on account parameters, instrument specifications, and personal risk tolerance. Keep that decision in your risk plan, not in a visual bias tool.
* Claims of edge. These measures summarize path geometry and trend context; they do not ensure a tradable edge on their own.
Summary of how to think about the output:
* The script builds a 12-step forward path by stacking linear-regression micro-forecasts across increasing multiples of the chart timeframe.
* Each micro-forecast is blended between trend and anti-trend using an adaptive ADX band with separate aggression controls for positive and negative regimes.
* All computations are done in ATR-true units for each timeframe before reconversion to price, ensuring dimensional consistency when accumulating steps.
* Bias% (per-timeframe and Meta) condenses directional efficiency and trend fidelity into a compact score.
* The output is designed to serve as an analytical overlay that helps assess whether conditions look trend-friendly, fade-friendly, or neutral, while acknowledging higher-timeframe update behavior and avoiding prescriptive trade rules.
Use this tool as one component within a disciplined process that includes independent confirmation, event awareness, and robust risk management.
Red & Green Zone ReversalOverview
The “Red & Green Zone Reversal” indicator is designed to visually highlight potential reversal zones on your chart by using a combination of Bollinger Bands and the Relative Strength Index (RSI).
It overlays on the chart and provides background color cues—red for oversold conditions and green for overbought conditions—along with corresponding alert triggers.
Key Components
Overlay: The indicator is set to overlay the chart, meaning its visual cues (colored backgrounds) are drawn directly on the price chart.
Bollinger Bands Calculation
Period: A 20-period simple moving average (SMA) is calculated from the closing prices.
Standard Deviation Multiplier: A multiplier of 2.0 is applied.
Bands Defined:
Basis: The 20-period SMA.
Deviation: Calculated as 2 times the standard deviation over the same period.
Upper Band: Basis plus the deviation.
Lower Band: Basis minus the deviation.
RSI Calculation
Period: The RSI is computed over a 14-period span using the closing prices.
Thresholds:
Oversold Threshold: 30 (used for the red zone condition).
Overbought Threshold: 70 (used for the green zone condition).
Zone Conditions
Red Zone (Oversold):
Criteria: The price is below the lower Bollinger Band and the RSI is below 30.
Purpose: Highlights a situation where the asset may be deeply oversold, signaling a potential reversal to the upside.
Green Zone (Overbought):
Criteria: The price is above the upper Bollinger Band and the RSI is above 70.
Purpose: Indicates that the asset may be overbought, potentially signaling a reversal to the downside.
Visual and Alert Components
Background Coloring:
Red Background: Applied when the red zone condition is met (using a semi-transparent red).
Green Background: Applied when the green zone condition is met (using a semi-transparent green).
Alerts:
Red Alert: An alert condition titled “Deep Oversold Alert” is triggered with the message “Deep Oversold Signal triggered!” when the red zone criteria are satisfied.
Green Alert: Similarly, an alert condition titled “Deep Overbought Alert” is triggered with the message “Deep Overbought Signal triggered!” when the green zone criteria are met.
Important Disclaimers
Not Financial Advice:
This indicator is provided for informational and analytical purposes only. It does not constitute trading advice or a recommendation to buy or sell any asset. Traders should use it as one of several tools in their analysis and should perform their own due diligence.
Risk Management:
Trading inherently involves risk. Past performance is not indicative of future results. Always implement appropriate risk management and use stop losses where necessary.
Summary
In summary, the “Red & Green Zone Reversal” indicator uses Bollinger Bands and RSI to detect extreme market conditions. It visually marks oversold (red) and overbought (green) conditions directly on the chart and offers alert conditions to help traders monitor these potential reversal points.
Enjoy!!
Quinn-Fernandes Fourier Transform of Filtered Price [Loxx]Down the Rabbit Hole We Go: A Deep Dive into the Mysteries of Quinn-Fernandes Fast Fourier Transform and Hodrick-Prescott Filtering
In the ever-evolving landscape of financial markets, the ability to accurately identify and exploit underlying market patterns is of paramount importance. As market participants continuously search for innovative tools to gain an edge in their trading and investment strategies, advanced mathematical techniques, such as the Quinn-Fernandes Fourier Transform and the Hodrick-Prescott Filter, have emerged as powerful analytical tools. This comprehensive analysis aims to delve into the rich history and theoretical foundations of these techniques, exploring their applications in financial time series analysis, particularly in the context of a sophisticated trading indicator. Furthermore, we will critically assess the limitations and challenges associated with these transformative tools, while offering practical insights and recommendations for overcoming these hurdles to maximize their potential in the financial domain.
Our investigation will begin with a comprehensive examination of the origins and development of both the Quinn-Fernandes Fourier Transform and the Hodrick-Prescott Filter. We will trace their roots from classical Fourier analysis and time series smoothing to their modern-day adaptive iterations. We will elucidate the key concepts and mathematical underpinnings of these techniques and demonstrate how they are synergistically used in the context of the trading indicator under study.
As we progress, we will carefully consider the potential drawbacks and challenges associated with using the Quinn-Fernandes Fourier Transform and the Hodrick-Prescott Filter as integral components of a trading indicator. By providing a critical evaluation of their computational complexity, sensitivity to input parameters, assumptions about data stationarity, performance in noisy environments, and their nature as lagging indicators, we aim to offer a balanced and comprehensive understanding of these powerful analytical tools.
In conclusion, this in-depth analysis of the Quinn-Fernandes Fourier Transform and the Hodrick-Prescott Filter aims to provide a solid foundation for financial market participants seeking to harness the potential of these advanced techniques in their trading and investment strategies. By shedding light on their history, applications, and limitations, we hope to equip traders and investors with the knowledge and insights necessary to make informed decisions and, ultimately, achieve greater success in the highly competitive world of finance.
█ Fourier Transform and Hodrick-Prescott Filter in Financial Time Series Analysis
Financial time series analysis plays a crucial role in making informed decisions about investments and trading strategies. Among the various methods used in this domain, the Fourier Transform and the Hodrick-Prescott (HP) Filter have emerged as powerful techniques for processing and analyzing financial data. This section aims to provide a comprehensive understanding of these two methodologies, their significance in financial time series analysis, and their combined application to enhance trading strategies.
█ The Quinn-Fernandes Fourier Transform: History, Applications, and Use in Financial Time Series Analysis
The Quinn-Fernandes Fourier Transform is an advanced spectral estimation technique developed by John J. Quinn and Mauricio A. Fernandes in the early 1990s. It builds upon the classical Fourier Transform by introducing an adaptive approach that improves the identification of dominant frequencies in noisy signals. This section will explore the history of the Quinn-Fernandes Fourier Transform, its applications in various domains, and its specific use in financial time series analysis.
History of the Quinn-Fernandes Fourier Transform
The Quinn-Fernandes Fourier Transform was introduced in a 1993 paper titled "The Application of Adaptive Estimation to the Interpolation of Missing Values in Noisy Signals." In this paper, Quinn and Fernandes developed an adaptive spectral estimation algorithm to address the limitations of the classical Fourier Transform when analyzing noisy signals.
The classical Fourier Transform is a powerful mathematical tool that decomposes a function or a time series into a sum of sinusoids, making it easier to identify underlying patterns and trends. However, its performance can be negatively impacted by noise and missing data points, leading to inaccurate frequency identification.
Quinn and Fernandes sought to address these issues by developing an adaptive algorithm that could more accurately identify the dominant frequencies in a noisy signal, even when data points were missing. This adaptive algorithm, now known as the Quinn-Fernandes Fourier Transform, employs an iterative approach to refine the frequency estimates, ultimately resulting in improved spectral estimation.
Applications of the Quinn-Fernandes Fourier Transform
The Quinn-Fernandes Fourier Transform has found applications in various fields, including signal processing, telecommunications, geophysics, and biomedical engineering. Its ability to accurately identify dominant frequencies in noisy signals makes it a valuable tool for analyzing and interpreting data in these domains.
For example, in telecommunications, the Quinn-Fernandes Fourier Transform can be used to analyze the performance of communication systems and identify interference patterns. In geophysics, it can help detect and analyze seismic signals and vibrations, leading to improved understanding of geological processes. In biomedical engineering, the technique can be employed to analyze physiological signals, such as electrocardiograms, leading to more accurate diagnoses and better patient care.
Use of the Quinn-Fernandes Fourier Transform in Financial Time Series Analysis
In financial time series analysis, the Quinn-Fernandes Fourier Transform can be a powerful tool for isolating the dominant cycles and frequencies in asset price data. By more accurately identifying these critical cycles, traders can better understand the underlying dynamics of financial markets and develop more effective trading strategies.
The Quinn-Fernandes Fourier Transform is used in conjunction with the Hodrick-Prescott Filter, a technique that separates the underlying trend from the cyclical component in a time series. By first applying the Hodrick-Prescott Filter to the financial data, short-term fluctuations and noise are removed, resulting in a smoothed representation of the underlying trend. This smoothed data is then subjected to the Quinn-Fernandes Fourier Transform, allowing for more accurate identification of the dominant cycles and frequencies in the asset price data.
By employing the Quinn-Fernandes Fourier Transform in this manner, traders can gain a deeper understanding of the underlying dynamics of financial time series and develop more effective trading strategies. The enhanced knowledge of market cycles and frequencies can lead to improved risk management and ultimately, better investment performance.
The Quinn-Fernandes Fourier Transform is an advanced spectral estimation technique that has proven valuable in various domains, including financial time series analysis. Its adaptive approach to frequency identification addresses the limitations of the classical Fourier Transform when analyzing noisy signals, leading to more accurate and reliable analysis. By employing the Quinn-Fernandes Fourier Transform in financial time series analysis, traders can gain a deeper understanding of the underlying financial instrument.
Drawbacks to the Quinn-Fernandes algorithm
While the Quinn-Fernandes Fourier Transform is an effective tool for identifying dominant cycles and frequencies in financial time series, it is not without its drawbacks. Some of the limitations and challenges associated with this indicator include:
1. Computational complexity: The adaptive nature of the Quinn-Fernandes Fourier Transform requires iterative calculations, which can lead to increased computational complexity. This can be particularly challenging when analyzing large datasets or when the indicator is used in real-time trading environments.
2. Sensitivity to input parameters: The performance of the Quinn-Fernandes Fourier Transform is dependent on the choice of input parameters, such as the number of harmonic periods, frequency tolerance, and Hodrick-Prescott filter settings. Choosing inappropriate parameter values can lead to inaccurate frequency identification or reduced performance. Finding the optimal parameter settings can be challenging, and may require trial and error or a more sophisticated optimization process.
3. Assumption of stationary data: The Quinn-Fernandes Fourier Transform assumes that the underlying data is stationary, meaning that its statistical properties do not change over time. However, financial time series data is often non-stationary, with changing trends and volatility. This can limit the effectiveness of the indicator and may require additional preprocessing steps, such as detrending or differencing, to ensure the data meets the assumptions of the algorithm.
4. Limitations in noisy environments: Although the Quinn-Fernandes Fourier Transform is designed to handle noisy signals, its performance may still be negatively impacted by significant noise levels. In such cases, the identification of dominant frequencies may become less reliable, leading to suboptimal trading signals or strategies.
5. Lagging indicator: As with many technical analysis tools, the Quinn-Fernandes Fourier Transform is a lagging indicator, meaning that it is based on past data. While it can provide valuable insights into historical market dynamics, its ability to predict future price movements may be limited. This can result in false signals or late entries and exits, potentially reducing the effectiveness of trading strategies based on this indicator.
Despite these drawbacks, the Quinn-Fernandes Fourier Transform remains a valuable tool for financial time series analysis when used appropriately. By being aware of its limitations and adjusting input parameters or preprocessing steps as needed, traders can still benefit from its ability to identify dominant cycles and frequencies in financial data, and use this information to inform their trading strategies.
█ Deep-dive into the Hodrick-Prescott Fitler
The Hodrick-Prescott (HP) filter is a statistical tool used in economics and finance to separate a time series into two components: a trend component and a cyclical component. It is a powerful tool for identifying long-term trends in economic and financial data and is widely used by economists, central banks, and financial institutions around the world.
The HP filter was first introduced in the 1990s by economists Robert Hodrick and Edward Prescott. It is a simple, two-parameter filter that separates a time series into a trend component and a cyclical component. The trend component represents the long-term behavior of the data, while the cyclical component captures the shorter-term fluctuations around the trend.
The HP filter works by minimizing the following objective function:
Minimize: (Sum of Squared Deviations) + λ (Sum of Squared Second Differences)
Where:
1. The first term represents the deviation of the data from the trend.
2. The second term represents the smoothness of the trend.
3. λ is a smoothing parameter that determines the degree of smoothness of the trend.
The smoothing parameter λ is typically set to a value between 100 and 1600, depending on the frequency of the data. Higher values of λ lead to a smoother trend, while lower values lead to a more volatile trend.
The HP filter has several advantages over other smoothing techniques. It is a non-parametric method, meaning that it does not make any assumptions about the underlying distribution of the data. It also allows for easy comparison of trends across different time series and can be used with data of any frequency.
Another significant advantage of the HP Filter is its ability to adapt to changes in the underlying trend. This feature makes it particularly well-suited for analyzing financial time series, which often exhibit non-stationary behavior. By employing the HP Filter to smooth financial data, traders can more accurately identify and analyze the long-term trends that drive asset prices, ultimately leading to better-informed investment decisions.
However, the HP filter also has some limitations. It assumes that the trend is a smooth function, which may not be the case in some situations. It can also be sensitive to changes in the smoothing parameter λ, which may result in different trends for the same data. Additionally, the filter may produce unrealistic trends for very short time series.
Despite these limitations, the HP filter remains a valuable tool for analyzing economic and financial data. It is widely used by central banks and financial institutions to monitor long-term trends in the economy, and it can be used to identify turning points in the business cycle. The filter can also be used to analyze asset prices, exchange rates, and other financial variables.
The Hodrick-Prescott filter is a powerful tool for analyzing economic and financial data. It separates a time series into a trend component and a cyclical component, allowing for easy identification of long-term trends and turning points in the business cycle. While it has some limitations, it remains a valuable tool for economists, central banks, and financial institutions around the world.
█ Combined Application of Fourier Transform and Hodrick-Prescott Filter
The integration of the Fourier Transform and the Hodrick-Prescott Filter in financial time series analysis can offer several benefits. By first applying the HP Filter to the financial data, traders can remove short-term fluctuations and noise, effectively isolating the underlying trend. This smoothed data can then be subjected to the Fourier Transform, allowing for the identification of dominant cycles and frequencies with greater precision.
By combining these two powerful techniques, traders can gain a more comprehensive understanding of the underlying dynamics of financial time series. This enhanced knowledge can lead to the development of more effective trading strategies, better risk management, and ultimately, improved investment performance.
The Fourier Transform and the Hodrick-Prescott Filter are powerful tools for financial time series analysis. Each technique offers unique benefits, with the Fourier Transform being adept at identifying dominant cycles and frequencies, and the HP Filter excelling at isolating long-term trends from short-term noise. By combining these methodologies, traders can develop a deeper understanding of the underlying dynamics of financial time series, leading to more informed investment decisions and improved trading strategies. As the financial markets continue to evolve, the combined application of these techniques will undoubtedly remain an essential aspect of modern financial analysis.
█ Features
Endpointed and Non-repainting
This is an endpointed and non-repainting indicator. These are crucial factors that contribute to its usefulness and reliability in trading and investment strategies. Let us break down these concepts and discuss why they matter in the context of a financial indicator.
1. Endpoint nature: An endpoint indicator uses the most recent data points to calculate its values, ensuring that the output is timely and reflective of the current market conditions. This is in contrast to non-endpoint indicators, which may use earlier data points in their calculations, potentially leading to less timely or less relevant results. By utilizing the most recent data available, the endpoint nature of this indicator ensures that it remains up-to-date and relevant, providing traders and investors with valuable and actionable insights into the market dynamics.
2. Non-repainting characteristic: A non-repainting indicator is one that does not change its values or signals after they have been generated. This means that once a signal or a value has been plotted on the chart, it will remain there, and future data will not affect it. This is crucial for traders and investors, as it offers a sense of consistency and certainty when making decisions based on the indicator's output.
Repainting indicators, on the other hand, can change their values or signals as new data comes in, effectively "repainting" the past. This can be problematic for several reasons:
a. Misleading results: Repainting indicators can create the illusion of a highly accurate or successful trading system when backtesting, as the indicator may adapt its past signals to fit the historical price data. This can lead to overly optimistic performance results that may not hold up in real-time trading.
b. Decision-making uncertainty: When an indicator repaints, it becomes challenging for traders and investors to trust its signals, as the signal that prompted a trade may change or disappear after the fact. This can create confusion and indecision, making it difficult to execute a consistent trading strategy.
The endpoint and non-repainting characteristics of this indicator contribute to its overall reliability and effectiveness as a tool for trading and investment decision-making. By providing timely and consistent information, this indicator helps traders and investors make well-informed decisions that are less likely to be influenced by misleading or shifting data.
Inputs
Source: This input determines the source of the price data to be used for the calculations. Users can select from options like closing price, opening price, high, low, etc., based on their preferences. Changing the source of the price data (e.g., from closing price to opening price) will alter the base data used for calculations, which may lead to different patterns and cycles being identified.
Calculation Bars: This input represents the number of past bars used for the calculation. A higher value will use more historical data for the analysis, while a lower value will focus on more recent price data. Increasing the number of past bars used for calculation will incorporate more historical data into the analysis. This may lead to a more comprehensive understanding of long-term trends but could also result in a slower response to recent price changes. Decreasing this value will focus more on recent data, potentially making the indicator more responsive to short-term fluctuations.
Harmonic Period: This input represents the harmonic period, which is the number of harmonics used in the Fourier Transform. A higher value will result in more harmonics being used, potentially capturing more complex cycles in the price data. Increasing the harmonic period will include more harmonics in the Fourier Transform, potentially capturing more complex cycles in the price data. However, this may also introduce more noise and make it harder to identify clear patterns. Decreasing this value will focus on simpler cycles and may make the analysis clearer, but it might miss out on more complex patterns.
Frequency Tolerance: This input represents the frequency tolerance, which determines how close the frequencies of the harmonics must be to be considered part of the same cycle. A higher value will allow for more variation between harmonics, while a lower value will require the frequencies to be more similar. Increasing the frequency tolerance will allow for more variation between harmonics, potentially capturing a broader range of cycles. However, this may also introduce noise and make it more difficult to identify clear patterns. Decreasing this value will require the frequencies to be more similar, potentially making the analysis clearer, but it might miss out on some cycles.
Number of Bars to Render: This input determines the number of bars to render on the chart. A higher value will result in more historical data being displayed, but it may also slow down the computation due to the increased amount of data being processed. Increasing the number of bars to render on the chart will display more historical data, providing a broader context for the analysis. However, this may also slow down the computation due to the increased amount of data being processed. Decreasing this value will speed up the computation, but it will provide less historical context for the analysis.
Smoothing Mode: This input allows the user to choose between two smoothing modes for the source price data: no smoothing or Hodrick-Prescott (HP) smoothing. The choice depends on the user's preference for how the price data should be processed before the Fourier Transform is applied. Choosing between no smoothing and Hodrick-Prescott (HP) smoothing will affect the preprocessing of the price data. Using HP smoothing will remove some of the short-term fluctuations from the data, potentially making the analysis clearer and more focused on longer-term trends. Not using smoothing will retain the original price fluctuations, which may provide more detail but also introduce noise into the analysis.
Hodrick-Prescott Filter Period: This input represents the Hodrick-Prescott filter period, which is used if the user chooses to apply HP smoothing to the price data. A higher value will result in a smoother curve, while a lower value will retain more of the original price fluctuations. Increasing the Hodrick-Prescott filter period will result in a smoother curve for the price data, emphasizing longer-term trends and minimizing short-term fluctuations. Decreasing this value will retain more of the original price fluctuations, potentially providing more detail but also introducing noise into the analysis.
Alets and signals
This indicator featues alerts, signals and bar coloring. You have to option to turn these on/off in the settings menu.
Maximum Bars Restriction
This indicator requires a large amount of processing power to render on the chart. To reduce overhead, the setting "Number of Bars to Render" is set to 500 bars. You can adjust this to you liking.
█ Related Indicators and Libraries
Goertzel Cycle Composite Wave
Goertzel Browser
Fourier Spectrometer of Price w/ Extrapolation Forecast
Fourier Extrapolator of 'Caterpillar' SSA of Price
Normalized, Variety, Fast Fourier Transform Explorer
Real-Fast Fourier Transform of Price Oscillator
Real-Fast Fourier Transform of Price w/ Linear Regression
Fourier Extrapolation of Variety Moving Averages
Fourier Extrapolator of Variety RSI w/ Bollinger Bands
Fourier Extrapolator of Price w/ Projection Forecast
Fourier Extrapolator of Price
STD-Stepped Fast Cosine Transform Moving Average
Variety RSI of Fast Discrete Cosine Transform
loxfft
harmonicpatterns1Library "harmonicpatterns1"
harmonicpatterns: methods required for calculation of harmonic patterns. Correction for library (missing export in line 303)
isGartleyPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isGartleyPattern: Checks for harmonic pattern Gartley
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Gartley. False otherwise.
isBatPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isBatPattern: Checks for harmonic pattern Bat
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Bat. False otherwise.
isButterflyPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isButterflyPattern: Checks for harmonic pattern Butterfly
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Butterfly. False otherwise.
isCrabPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isCrabPattern: Checks for harmonic pattern Crab
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Crab. False otherwise.
isDeepCrabPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isDeepCrabPattern: Checks for harmonic pattern DeepCrab
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is DeepCrab. False otherwise.
isCypherPattern(xabRatio, axcRatio, xadRatio, err_min, err_max) isCypherPattern: Checks for harmonic pattern Cypher
Parameters:
xabRatio : AB/XA
axcRatio : XC/AX
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Cypher. False otherwise.
isSharkPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isSharkPattern: Checks for harmonic pattern Shark
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Shark. False otherwise.
isNenStarPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isNenStarPattern: Checks for harmonic pattern Nenstar
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Nenstar. False otherwise.
isAntiNenStarPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isAntiNenStarPattern: Checks for harmonic pattern Anti NenStar
Parameters:
xabRatio : - AB/XA
abcRatio : - BC/AB
bcdRatio : - CD/BC
xadRatio : - AD/XA
err_min : - Minumum error threshold
err_max : - Maximum error threshold
Returns: True if the pattern is Anti NenStar. False otherwise.
isAntiSharkPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isAntiSharkPattern: Checks for harmonic pattern Anti Shark
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Anti Shark. False otherwise.
isAntiCypherPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isAntiCypherPattern: Checks for harmonic pattern Anti Cypher
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Anti Cypher. False otherwise.
isAntiCrabPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isAntiCrabPattern: Checks for harmonic pattern Anti Crab
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Anti Crab. False otherwise.
isAntiButterflyPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isAntiButterflyPattern: Checks for harmonic pattern Anti Butterfly
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Anti Butterfly. False otherwise.
isAntiBatPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isAntiBatPattern: Checks for harmonic pattern Anti Bat
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Anti Bat. False otherwise.
isAntiGartleyPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isAntiGartleyPattern: Checks for harmonic pattern Anti Gartley
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Anti Gartley. False otherwise.
isNavarro200Pattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isNavarro200Pattern: Checks for harmonic pattern Navarro200
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Navarro200. False otherwise.
isHarmonicPattern(x, a, c, c, d, flags, errorPercent) isHarmonicPattern: Checks for harmonic patterns
Parameters:
x : X coordinate value
a : A coordinate value
c : B coordinate value
c : C coordinate value
d : D coordinate value
flags : flags to check patterns. Send empty array to enable all
errorPercent : Error threshold
Returns: Array of boolean values which says whether valid pattern exist and array of corresponding pattern names
harmonicpatternsLibrary "harmonicpatterns"
harmonicpatterns: methods required for calculation of harmonic patterns. These are customised to be used in my scripts. But, also simple enough for others to make use of :)
isGartleyPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isGartleyPattern: Checks for harmonic pattern Gartley
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Gartley. False otherwise.
isBatPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isBatPattern: Checks for harmonic pattern Bat
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Bat. False otherwise.
isButterflyPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isButterflyPattern: Checks for harmonic pattern Butterfly
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Butterfly. False otherwise.
isCrabPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isCrabPattern: Checks for harmonic pattern Crab
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Crab. False otherwise.
isDeepCrabPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isDeepCrabPattern: Checks for harmonic pattern DeepCrab
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is DeepCrab. False otherwise.
isCypherPattern(xabRatio, axcRatio, xadRatio, err_min, err_max) isCypherPattern: Checks for harmonic pattern Cypher
Parameters:
xabRatio : AB/XA
axcRatio : XC/AX
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Cypher. False otherwise.
isSharkPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isSharkPattern: Checks for harmonic pattern Shark
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Shark. False otherwise.
isNenStarPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isNenStarPattern: Checks for harmonic pattern Nenstar
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Nenstar. False otherwise.
isAntiNenStarPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isAntiNenStarPattern: Checks for harmonic pattern Anti NenStar
Parameters:
xabRatio : - AB/XA
abcRatio : - BC/AB
bcdRatio : - CD/BC
xadRatio : - AD/XA
err_min : - Minumum error threshold
err_max : - Maximum error threshold
Returns: True if the pattern is Anti NenStar. False otherwise.
isAntiSharkPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isAntiSharkPattern: Checks for harmonic pattern Anti Shark
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Anti Shark. False otherwise.
isAntiCypherPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isAntiCypherPattern: Checks for harmonic pattern Anti Cypher
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Anti Cypher. False otherwise.
isAntiCrabPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isAntiCrabPattern: Checks for harmonic pattern Anti Crab
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Anti Crab. False otherwise.
isAntiBatPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isAntiBatPattern: Checks for harmonic pattern Anti Bat
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Anti Bat. False otherwise.
isAntiGartleyPattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isAntiGartleyPattern: Checks for harmonic pattern Anti Gartley
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Anti Gartley. False otherwise.
isNavarro200Pattern(xabRatio, abcRatio, bcdRatio, xadRatio, err_min, err_max) isNavarro200Pattern: Checks for harmonic pattern Navarro200
Parameters:
xabRatio : AB/XA
abcRatio : BC/AB
bcdRatio : CD/BC
xadRatio : AD/XA
err_min : Minumum error threshold
err_max : Maximum error threshold
Returns: True if the pattern is Navarro200. False otherwise.
isHarmonicPattern(x, a, c, c, d, flags, errorPercent) isHarmonicPattern: Checks for harmonic patterns
Parameters:
x : X coordinate value
a : A coordinate value
c : B coordinate value
c : C coordinate value
d : D coordinate value
flags : flags to check patterns. Send empty array to enable all
errorPercent : Error threshold
Returns: Array of boolean values which says whether valid pattern exist and array of corresponding pattern names
Sector Rotation & Money Flow Dashboard📊 Overview
The Sector Rotation & Money Flow Dashboard is a comprehensive market analysis tool that tracks 39 major sector ETFs in real-time, providing institutional-grade insights into sector rotation, momentum shifts, and money flow patterns. This indicator helps traders identify which sectors are attracting capital, which are losing favor, and where the next opportunities might emerge.
Perfect for swing traders, position traders, and investors who want to stay ahead of sector rotation and ride the strongest trends while avoiding weak sectors.
🎯 What This Indicator Does
Tracks 39 Major Sectors: From technology to utilities, cryptocurrencies to commodities
Calculates Multiple Timeframes: 1-week, 1-month, 3-month, and 6-month performance
Advanced Momentum Metrics: Proprietary momentum score and acceleration calculations
Relative Strength Analysis: Compare sector performance against any benchmark index
Money Flow Signals: Visual indicators showing where institutional money is moving
Smart Filtering: Pre-built strategy filters for different trading styles
Trend Detection: Emoji-based visual system for quick trend identification
💡 Key Features
1. Performance Metrics
Multiple timeframe analysis (1W, 1M, 3M, 6M)
Month-over-month change tracking
Relative strength vs benchmark index
2. Advanced Analytics
Momentum Score: Weighted composite of recent performance
Acceleration: Rate of change in momentum (second derivative)
Money Flow Signals: IN/OUT/TURN/WATCH indicators
3. Strategy Preset Filters
🎯 Swing Trade: High momentum opportunities
📈 Trend Follow: Established uptrends
🔄 Mean Reversion: Oversold bounce candidates
💎 Value Hunt: Deep value opportunities
🚀 Breakout: Emerging strength
⚠️ Risk Off: Sectors to avoid
4. Customization
All 39 sector ETFs can be customized
Adjustable benchmark index
Flexible display options
Multiple sorting methods
📋 Settings Documentation
Display Settings
Show Table (Default: On)
Toggles the entire dashboard display
Table Position (Default: Middle Center)
Choose from 9 positions on your chart
Options: Top/Middle/Bottom × Left/Center/Right
Rows to Show (Default: 15)
Number of sectors displayed (5-40)
Useful for focusing on top/bottom performers
Sort By (Default: Momentum)
1M/3M/6M: Sort by specific timeframe performance
Momentum: Weighted recent performance score
Acceleration: Rate of momentum change
1M Change: Month-over-month improvement
RS: Relative strength vs benchmark
Flow: IN First: Prioritize sectors with inflows
Flow: TURN First: Focus on reversal candidates
Recovery Plays: Oversold sectors recovering
Oversold Bounce: Deepest declines with positive signs
Top Gainers/Losers 3M: Best/worst quarterly performers
Best Acc + Mom: Combined strength score
Worst Acc (Topping): Sectors losing momentum
Filter Settings
Strategy Preset Filter (Default: All)
All: No filtering
🎯 Swing Trade: Mom >5, Acc >2, Money flowing in
📈 Trend Follow: Positive 1M & 3M, RS >0
🔄 Mean Reversion: Oversold but improving
💎 Value Hunt: Down >10% with recovery signs
🚀 Breakout: Rapid momentum surge
⚠️ Risk Off: Declining or topping sectors
Custom Flow Filter: Use manual flow filter
Custom Flow Signal Filter (Default: All)
Only active when Strategy Preset = "Custom Flow Filter"
IN Only: Strong inflows
TURN Only: Reversal signals
WATCH Only: Recovery candidates
OUT Only: Outflow sectors
Active Flows Only: Any non-neutral signal
Hide Low Volume ETFs (Default: Off)
Filters out illiquid sectors (future enhancement)
Visual Settings
Show Trend Emojis (Default: On)
🚀 Breakout (Strong 1M + High Acceleration)
🔥 Hot Recovery (From -10% to positive)
💪 Steady Uptrend (All timeframes positive)
➡️ Sideways/Ranging
⚠️ Warning/Topping (Up >15%, now slowing)
📉 Falling (Negative + declining)
🔄 Bottoming (Improving from lows)
Compact Mode (Default: Off)
Removes decimals for cleaner display
Useful when showing many rows
Min Data Points Required (Default: 3)
Minimum data points needed to display a sector
Prevents showing sectors with insufficient data
Relative Strength Settings
RS Benchmark Index (Default: AMEX:SPY)
Index to compare all sectors against
Can use SPY, QQQ, IWM, or any other index
RS Period (Days) (Default: 21)
Lookback period for RS calculation
21 days = 1 month, 63 days = 3 months, etc.
Sector ETF Settings (Groups 1-39)
Each sector has two inputs:
Symbol: The ticker (e.g., "AMEX:XLF")
Name: Display name (e.g., "Financials")
All 39 sectors can be customized to track different ETFs or markets.
📈 Column Explanations
Sector: ETF name/description
1M%: 1-month (21-day) performance
3M%: 3-month (63-day) performance
6M%: 6-month (126-day) performance
Mom: Momentum score (weighted average, recent-biased)
Acc: Acceleration (momentum rate of change)
Δ1M: Month-over-month change
RS: Relative strength vs benchmark
Flow: Money flow signal
↗️ IN: Strong inflows
🔄 TURN: Potential reversal
👀 WATCH: Recovery candidate
↘️ OUT: Outflows
—: Neutral
🎮 Usage Tips
For Swing Traders (3-14 days)
Use "🎯 Swing Trade" filter
Sort by "Acceleration" or "Momentum"
Look for Flow = "IN" and Mom >10
Confirm with positive RS
For Position Traders (2-8 weeks)
Use "📈 Trend Follow" filter
Sort by "RS" or "Best Acc + Mom"
Focus on consistent green across timeframes
Ensure RS >3 for market leaders
For Value Investors
Use "💎 Value Hunt" filter
Sort by "Recovery Plays" or "Top Losers 3M"
Look for improving Δ1M
Check for "WATCH" or "TURN" signals
For Risk Management
Regularly check "⚠️ Risk Off" filter
Sort by "Worst Acc (Topping)"
Review holdings for ⚠️ warning emojis
Exit sectors showing "OUT" flow
Market Regime Recognition
Bull Market: Many sectors showing "IN" flow, positive RS
Bear Market: Widespread "OUT" flows, negative RS
Rotation: Mixed flows, some "IN" while others "OUT"
Recovery: Multiple "TURN" and "WATCH" signals
🔧 Pro Tips
Combine Filters + Sorting: Filter first to narrow candidates, then sort to prioritize
Multi-Timeframe Confirmation: Best setups show alignment across 1M, 3M, and momentum
RS is Key: Sectors outperforming SPY (RS >0) tend to continue outperforming
Acceleration Matters: Positive acceleration often precedes price breakouts
Flow Transitions: "WATCH" → "TURN" → "IN" progression identifies new trends early
Regular Scans:
Daily: Check "Acceleration" sort
Weekly: Review "1M Change"
Monthly: Analyze "RS" shifts
Divergence Signals:
Price up but Acceleration down = Potential top
Price down but Acceleration up = Potential bottom
Sector Pairs Trading: Long sectors with "IN" flow, short sectors with "OUT" flow
⚠️ Important Notes
This indicator makes 40 security requests (maximum allowed)
Best used on Daily timeframe
Data updates in real-time during market hours
Some ETFs may show "—" if data is unavailable
🎯 Common Strategies
"Follow the Flow"
Only trade sectors showing "IN" flow with positive RS
"Rotation Catcher"
Focus on "TURN" signals in sectors down >15% from highs
"Momentum Rider"
Trade top 3 sectors by Momentum score, exit when Acceleration turns negative
"Mean Reversion"
Buy sectors in bottom 20% by 3M performance when Δ1M improves
"Relative Strength Leader"
Maintain positions only in sectors with RS >5
Not financial advice - always do additional research
Inflection PointInflection Point - The Adaptive Confluence Reversal Engine
This is not just another peak and valley indicator; it is a complete and total reimagining of how market turning points are detected, qualified, and acted upon. Born from the foundational concepts explored in systems like my earlier creation, DAFE - Turning Point, Inflection Point is a ground-up engineering feat designed for the modern trader. It moves beyond static rules and simple pattern recognition into the realm of dynamic, multi-factor confluence analysis and adaptive machine learning.
Where other indicators provide a guess, Inflection Point provides a probability. It meticulously analyzes the market's deepest currents—momentum, exhaustion, and reversal velocity—and fuses them into a single, unified "Confluence Score." This is not a simple combination of indicators; it is an intelligent, weighted system where each component works in concert, creating an analytical engine that is orders of magnitude more sophisticated and reliable than any standard reversal tool.
Furthermore, Inflection Point learns. Through its advanced Adaptive Learning Engine, it constantly monitors its own performance, adjusting its confidence and selectivity in real-time based on its recent success rate. This allows it to adapt its behavior to any security, on any timeframe, with remarkable success.
Theoretical Foundation - Confluence Core
Inflection Point's predictive power does not come from a single, magical formula. It comes from the intelligent synthesis of three critical market phenomena, weighted and scored in real-time to generate a single, high-conviction probability rating.
1. Factor One: Pre-Reversal Momentum State (RSI Analysis)
Instead of reacting to a simple RSI cross, Inflection Point proactively scans for the build-up of momentum that precedes a reversal.
• Formulaic Concept: It measures the highest RSI value over a lookback period for peaks and the lowest RSI for valleys. A signal is only considered valid if significant momentum has been established before the turn, indicating a stretched market condition ripe for reversal.
• Asymmetric Sophistication: The engine uses different, optimized thresholds for bull and bear momentum, recognizing that markets often fall faster than they rise.
2. Factor Two: Volatility Exhaustion (Bollinger Band Analysis)
A true reversal often occurs when price makes a final, exhaustive push into unsustainable territory.
• Formulaic Concept: The engine detects when price has significantly pierced the outer Bollinger Bands. This is not just a touch, but a statistical deviation from the mean that signals volatility exhaustion, where the energy for the current move is likely depleted.
3. Factor Three: Reversal Strength (Rate of Change Analysis)
The character of a reversal matters. A sharp, decisive turn is more significant than a slow, meandering one.
• Formulaic Concept: Using a short-term Rate of Change (ROC), the engine measures the velocity of the reversal itself. A higher ROC score adds significant weight to the final probability, confirming that the new direction has conviction.
4. The Final Calculation: The Adaptive Learning Engine
This is the system's "brain." It maintains a history of its past signals and calculates its real-time win rate. This hitRate is then used to generate an adaptiveMultiplier.
• Self-Correction: In "Quality Control" mode, a high win rate makes the indicator more selective, demanding a higher probability score to issue a signal, thereby protecting streaks. A lower win rate makes it slightly less selective to ensure it continues learning from new market conditions.
• The result is a system that is not static, but a living, breathing tool that adapts its personality to the unique rhythm of any chart.
Why Inflection Point is a Paradigm Shift
Inflection Point is fundamentally different from other reversal indicators for three key reasons:
Confluence Over Isolation: Standard indicators look at one thing (e.g., RSI > 70). Inflection Point simultaneously analyzes momentum, volatility, and velocity, understanding that true reversals are a product of multiple converging factors. It answers not just "if," but "why" a reversal is likely.
Probabilistic Over Binary: Other tools give you a simple "yes" or "no." Inflection Point provides a probability score from 0-100, allowing you to gauge the conviction of every potential signal. This empowers you to differentiate between a weak setup and an A+ opportunity.
Adaptive Over Static: Every other indicator uses the same rules forever. Inflection Point's Adaptive Engine means it is constantly refining its own logic based on what is actually working in the current market, on the specific asset you are trading. It is tailored to the now.
The Inputs Menu - Your Command Center
Every setting is a lever of control, allowing you to tune the engine to your precise trading style and market focus.
🧠 Neural Core Engine
Analysis Depth: This is the primary lookback for the Bollinger Band and other core calculations. A shorter depth makes the indicator faster and more sensitive, ideal for scalping. A longer depth makes it slower and more stable, ideal for swing trading.
Minimum Probability %: This is your master signal filter. It sets the minimum Confluence Score required to plot a signal. Higher values (85-95) will give you only the highest-conviction A+ setups. Lower values (70-80) will show more potential opportunities.
🤖 Adaptive Neural Learning
Enable Adaptive Learning Engine: Toggles the entire learning system. Disabling it will make the indicator's logic static.
Peak/Valley Success Threshold (ATR): This defines what constitutes a "successful" trade for the learning engine. A value of 1.5 means price must move 1.5x the ATR in your favor for the signal to be marked as a win. Adjust this to match your personal take-profit strategy.
Adaptive Mode: This dictates how the engine uses its hitRate. "Quality Control" is recommended for its intelligent filtering. "Aggressive" will always boost signal scores, useful for finding more setups in a known, trending environment.
Asymmetric Balance: Allows you to apply a "boost" to either peak (short) or valley (long) signals. If you find the market you're trading has stronger long reversals, you can increase the "Valley Signal Boost" to catch them more effectively.
🛡️ Elite Filters
Market Noise Filter: An exceptional tool for avoiding choppy markets. It counts the number of directional changes in the last 5 bars. If the market is whipping back and forth too much, it will block the signal. Lower the "Max Direction Changes" to be extremely selective.
Volume Filter: Requires signal confirmation from a significant volume spike. The "Volume Multiplier" dictates how large this spike must be (e.g., 1.2 = 20% above average volume). This is invaluable for filtering out low-conviction moves in stocks and crypto.
The Dashboard - Your Analytical Co-Pilot
The dashboard is not just a set of numbers; it is a holistic overview of the market's health and the engine's current state.
Unified AI Score: This section provides the most critical, at-a-glance information. "Total Score" is the current probability reading, while "Quality" gives you a human-readable interpretation. "Win Rate" shows the real-time performance of the Adaptive Engine.
Order Flow (OFPI): This measures the "weight" of money behind recent price moves by analyzing price change relative to volume. A high positive OFPI suggests strong buying pressure, while a high negative value suggests strong selling pressure. It gives you a peek into the market's underlying flow.
Component Analysis: This allows you to see the individual "Peak" and "Valley" confidence scores before they are filtered, giving you insight into building momentum before a signal forms.
Market Structure: This panel assesses the broader environment. "HTF Trend" tells you the direction of the larger trend (based on EMAs), while "Vol Regime" tells you if the market is in a high, medium, or low volatility state. Use this to align your signals with the broader market context.
Filter & Engine Statistics: Available on the "Large" dashboard, this provides deep insight into how many signals are being blocked by your filters and the current status of the Adaptive Engine's multiplier.
The Visual Interface - A Symphony of Data
Every visual element on the chart is designed for instant interpretation and insight.
Signal Markers: Simple, clean triangles mark the exact bar of a valid signal. A box is drawn around the high/low of the signal bar to highlight the precise point of inflection.
Dynamic Support/Resistance Zones: These are the glowing lines on your chart. They are not static lines; they are dynamic levels that represent the current battlefield between buyers and sellers.
Cyber Cyan (Valley Blue): This is the current Support Zone. This is the price level the market is currently trying to defend.
Neural Pink (Peak Red): This is the current Resistance Zone. This is the price level the market is currently trying to break through.
Grey (Next Level): This line is a projection, based on the current momentum and the size of the S/R range, of where the next major level of conflict will likely be. It acts as a potential price target.
Development & Philosophy
Inflection Point was not assembled; it was engineered. It represents hundreds of hours of research into market dynamics, statistical analysis, and machine learning principles. The goal was to create a tool that moves beyond the limitations of traditional technical analysis, which often fails in modern, algorithm-driven markets. By building a system based on multi-factor confluence and self-adaptive logic, Inflection Point provides a quantifiable, statistical edge that is simply unattainable with simpler tools. This is the result of a relentless pursuit of a better, more intelligent way to trade.
Universal Applicability
The principles of momentum, exhaustion, and velocity are universal to all freely traded markets. Because of its adaptive core and robust filtering options, Inflection Point has proven to be exceptionally effective on any security (stocks, crypto, forex, indices, futures) and on any timeframe (from 1-minute scalping charts to daily swing trading charts).
" Markets are constantly in a state of uncertainty and flux and money is made by discounting the obvious and betting on the unexpected. "
— George Soros
Trade with insight. Trade with anticipation.
— Dskyz, for DAFE Trading Systems
VoVix DEVMA🌌 VoVix DEVMA: A Deep Dive into Second-Order Volatility Dynamics
Welcome to VoVix+, a sophisticated trading framework that transcends traditional price analysis. This is not merely another indicator; it is a complete system designed to dissect and interpret the very fabric of market volatility. VoVix+ operates on the principle that the most powerful signals are not found in price alone, but in the behavior of volatility itself. It analyzes the rate of change, the momentum, and the structure of market volatility to identify periods of expansion and contraction, providing a unique edge in anticipating major market moves.
This document will serve as your comprehensive guide, breaking down every mathematical component, every user input, and every visual element to empower you with a profound understanding of how to harness its capabilities.
🔬 THEORETICAL FOUNDATION: THE MATHEMATICS OF MARKET DYNAMICS
VoVix+ is built upon a multi-layered mathematical engine designed to measure what we call "second-order volatility." While standard indicators analyze price, and first-order volatility indicators (like ATR) analyze the range of price, VoVix+ analyzes the dynamics of the volatility itself. This provides insight into the market's underlying state of stability or chaos.
1. The VoVix Score: Measuring Volatility Thrust
The core of the system begins with the VoVix Score. This is a normalized measure of volatility acceleration or deceleration.
Mathematical Formula:
VoVix Score = (ATR(fast) - ATR(slow)) / (StDev(ATR(fast)) + ε)
Where:
ATR(fast) is the Average True Range over a short period, representing current, immediate volatility.
ATR(slow) is the Average True Range over a longer period, representing the baseline or established volatility.
StDev(ATR(fast)) is the Standard Deviation of the fast ATR, which measures the "noisiness" or consistency of recent volatility.
ε (epsilon) is a very small number to prevent division by zero.
Market Implementation:
Positive Score (Expansion): When the fast ATR is significantly higher than the slow ATR, it indicates a rapid increase in volatility. The market is "stretching" or expanding.
Negative Score (Contraction): When the fast ATR falls below the slow ATR, it indicates a decrease in volatility. The market is "coiling" or contracting.
Normalization: By dividing by the standard deviation, we normalize the score. This turns it into a standardized measure, allowing us to compare volatility thrust across different market conditions and timeframes. A score of 2.0 in a quiet market means the same, relatively, as a score of 2.0 in a volatile market.
2. Deviation Analysis (DEV): Gauging Volatility's Own Volatility
The script then takes the analysis a step further. It calculates the standard deviation of the VoVix Score itself.
Mathematical Formula:
DEV = StDev(VoVix Score, lookback_period)
Market Implementation:
This DEV value represents the magnitude of chaos or stability in the market's volatility dynamics. A high DEV value means the volatility thrust is erratic and unpredictable. A low DEV value suggests the change in volatility is smooth and directional.
3. The DEVMA Crossover: Identifying Regime Shifts
This is the primary signal generator. We take two moving averages of the DEV value.
Mathematical Formula:
fastDEVMA = SMA(DEV, fast_period)
slowDEVMA = SMA(DEV, slow_period)
The Core Signal:
The strategy triggers on the crossover and crossunder of these two DEVMA lines. This is a profound concept: we are not looking at a moving average of price or even of volatility, but a moving average of the standard deviation of the normalized rate of change of volatility.
Bullish Crossover (fastDEVMA > slowDEVMA): This signals that the short-term measure of volatility's chaos is increasing relative to the long-term measure. This often precedes a significant market expansion and is interpreted as a bullish volatility regime.
Bearish Crossunder (fastDEVMA < slowDEVMA): This signals that the short-term measure of volatility's chaos is decreasing. The market is settling down or contracting, often leading to trending moves or range consolidation.
⚙️ INPUTS MENU: CONFIGURING YOUR ANALYSIS ENGINE
Every input has been meticulously designed to give you full control over the strategy's behavior. Understanding these settings is key to adapting VoVix+ to your specific instrument, timeframe, and trading style.
🌀 VoVix DEVMA Configuration
🧬 Deviation Lookback: This sets the lookback period for calculating the DEV value. It defines the window for measuring the stability of the VoVix Score. A shorter value makes the system highly reactive to recent changes in volatility's character, ideal for scalping. A longer value provides a smoother, more stable reading, better for identifying major, long-term regime shifts.
⚡ Fast VoVix Length: This is the lookback period for the fastDEVMA. It represents the short-term trend of volatility's chaos. A smaller number will result in a faster, more sensitive signal line that reacts quickly to market shifts.
🐌 Slow VoVix Length: This is the lookback period for the slowDEVMA. It represents the long-term, baseline trend of volatility's chaos. A larger number creates a more stable, slower-moving anchor against which the fast line is compared.
How to Optimize: The relationship between the Fast and Slow lengths is crucial. A wider gap (e.g., 20 and 60) will result in fewer, but potentially more significant, signals. A narrower gap (e.g., 25 and 40) will generate more frequent signals, suitable for more active trading styles.
🧠 Adaptive Intelligence
🧠 Enable Adaptive Features: When enabled, this activates the strategy's performance tracking module. The script will analyze the outcome of its last 50 trades to calculate a dynamic win rate.
⏰ Adaptive Time-Based Exit: If Enable Adaptive Features is on, this allows the strategy to adjust its Maximum Bars in Trade setting based on performance. It learns from the average duration of winning trades. If winning trades tend to be short, it may shorten the time exit to lock in profits. If winners tend to run, it will extend the time exit, allowing trades more room to develop. This helps prevent the strategy from cutting winning trades short or holding losing trades for too long.
⚡ Intelligent Execution
📊 Trade Quantity: A straightforward input that defines the number of contracts or shares for each trade. This is a fixed value for consistent position sizing.
🛡️ Smart Stop Loss: Enables the dynamic stop-loss mechanism.
🎯 Stop Loss ATR Multiplier: Determines the distance of the stop loss from the entry price, calculated as a multiple of the current 14-period ATR. A higher multiplier gives the trade more room to breathe but increases risk per trade. A lower multiplier creates a tighter stop, reducing risk but increasing the chance of being stopped out by normal market noise.
💰 Take Profit ATR Multiplier: Sets the take profit target, also as a multiple of the ATR. A common practice is to set this higher than the Stop Loss multiplier (e.g., a 2:1 or 3:1 reward-to-risk ratio).
🏃 Use Trailing Stop: This is a powerful feature for trend-following. When enabled, instead of a fixed stop loss, the stop will trail behind the price as the trade moves into profit, helping to lock in gains while letting winners run.
🎯 Trail Points & 📏 Trail Offset ATR Multipliers: These control the trailing stop's behavior. Trail Points defines how much profit is needed before the trail activates. Trail Offset defines how far the stop will trail behind the current price. Both are based on ATR, making them fully adaptive to market volatility.
⏰ Maximum Bars in Trade: This is a time-based stop. It forces an exit if a trade has been open for a specified number of bars, preventing positions from being held indefinitely in stagnant markets.
⏰ Session Management
These inputs allow you to confine the strategy's trading activity to specific market hours, which is crucial for day trading instruments that have defined high-volume sessions (e.g., stock market open).
🎨 Visual Effects & Dashboard
These toggles give you complete control over the on-chart visuals and the dashboard. You can disable any element to declutter your chart or focus only on the information that matters most to you.
📊 THE DASHBOARD: YOUR AT-A-GLANCE COMMAND CENTER
The dashboard centralizes all critical information into one compact, easy-to-read panel. It provides a real-time summary of the market state and strategy performance.
🎯 VOVIX ANALYSIS
Fast & Slow: Displays the current numerical values of the fastDEVMA and slowDEVMA. The color indicates their direction: green for rising, red for falling. This lets you see the underlying momentum of each line.
Regime: This is your most important environmental cue. It tells you the market's current state based on the DEVMA relationship. 🚀 EXPANSION (Green) signifies a bullish volatility regime where explosive moves are more likely. ⚛️ CONTRACTION (Purple) signifies a bearish volatility regime, where the market may be consolidating or entering a smoother trend.
Quality: Measures the strength of the last signal based on the magnitude of the DEVMA difference. An ELITE or STRONG signal indicates a high-conviction setup where the crossover had significant force.
PERFORMANCE
Win Rate & Trades: Displays the historical win rate of the strategy from the backtest, along with the total number of closed trades. This provides immediate feedback on the strategy's historical effectiveness on the current chart.
EXECUTION
Trade Qty: Shows your configured position size per trade.
Session: Indicates whether trading is currently OPEN (allowed) or CLOSED based on your session management settings.
POSITION
Position & PnL: Displays your current position (LONG, SHORT, or FLAT) and the real-time Profit or Loss of the open trade.
🧠 ADAPTIVE STATUS
Stop/Profit Mult: In this simplified version, these are placeholders. The primary adaptive feature currently modifies the time-based exit, which is reflected in how long trades are held on the chart.
🎨 THE VISUAL UNIVERSE: DECIPHERING MARKET GEOMETRY
The visuals are not mere decorations; they are geometric representations of the underlying mathematical concepts, designed to give you an intuitive feel for the market's state.
The Core Lines:
FastDEVMA (Green/Maroon Line): The primary signal line. Green when rising, indicating an increase in short-term volatility chaos. Maroon when falling.
SlowDEVMA (Aqua/Orange Line): The baseline. Aqua when rising, indicating a long-term increase in volatility chaos. Orange when falling.
🌊 Morphism Flow (Flowing Lines with Circles):
What it represents: This visualizes the momentum and strength of the fastDEVMA. The width and intensity of the "beam" are proportional to the signal strength.
Interpretation: A thick, steep, and vibrant flow indicates powerful, committed momentum in the current volatility regime. The floating '●' particles represent kinetic energy; more particles suggest stronger underlying force.
📐 Homotopy Paths (Layered Transparent Boxes):
What it represents: These layered boxes are centered between the two DEVMA lines. Their height is determined by the DEV value.
Interpretation: This visualizes the overall "volatility of volatility." Wider boxes indicate a chaotic, unpredictable market. Narrower boxes suggest a more stable, predictable environment.
🧠 Consciousness Field (The Grid):
What it represents: This grid provides a historical lookback at the DEV range.
Interpretation: It maps the recent "consciousness" or character of the market's volatility. A consistently wide grid suggests a prolonged period of chaos, while a narrowing grid can signal a transition to a more stable state.
📏 Functorial Levels (Projected Horizontal Lines):
What it represents: These lines extend from the current fastDEVMA and slowDEVMA values into the future.
Interpretation: Think of these as dynamic support and resistance levels for the volatility structure itself. A crossover becomes more significant if it breaks cleanly through a prior established level.
🌊 Flow Boxes (Spaced Out Boxes):
What it represents: These are compact visual footprints of the current regime, colored green for Expansion and red for Contraction.
Interpretation: They provide a quick, at-a-glance confirmation of the dominant volatility flow, reinforcing the background color.
Background Color:
This provides an immediate, unmistakable indication of the current volatility regime. Light Green for Expansion and Light Aqua/Blue for Contraction, allowing you to assess the market environment in a split second.
📊 BACKTESTING PERFORMANCE REVIEW & ANALYSIS
The following is a factual, transparent review of a backtest conducted using the strategy's default settings on a specific instrument and timeframe. This information is presented for educational purposes to demonstrate how the strategy's mechanics performed over a historical period. It is crucial to understand that these results are historical, apply only to the specific conditions of this test, and are not a guarantee or promise of future performance. Market conditions are dynamic and constantly change.
Test Parameters & Conditions
To ensure the backtest reflects a degree of real-world conditions, the following parameters were used. The goal is to provide a transparent baseline, not an over-optimized or unrealistic scenario.
Instrument: CME E-mini Nasdaq 100 Futures (NQ1!)
Timeframe: 5-Minute Chart
Backtesting Range: March 24, 2024, to July 09, 2024
Initial Capital: $100,000
Commission: $0.62 per contract (A realistic cost for futures trading).
Slippage: 3 ticks per trade (A conservative setting to account for potential price discrepancies between order placement and execution).
Trade Size: 1 contract per trade.
Performance Overview (Historical Data)
The test period generated 465 total trades , providing a statistically significant sample size for analysis, which is well above the recommended minimum of 100 trades for a strategy evaluation.
Profit Factor: The historical Profit Factor was 2.663 . This metric represents the gross profit divided by the gross loss. In this test, it indicates that for every dollar lost, $2.663 was gained.
Percent Profitable: Across all 465 trades, the strategy had a historical win rate of 84.09% . While a high figure, this is a historical artifact of this specific data set and settings, and should not be the sole basis for future expectations.
Risk & Trade Characteristics
Beyond the headline numbers, the following metrics provide deeper insight into the strategy's historical behavior.
Sortino Ratio (Downside Risk): The Sortino Ratio was 6.828 . Unlike the Sharpe Ratio, this metric only measures the volatility of negative returns. A higher value, such as this one, suggests that during this test period, the strategy was highly efficient at managing downside volatility and large losing trades relative to the profits it generated.
Average Trade Duration: A critical characteristic to understand is the strategy's holding period. With an average of only 2 bars per trade , this configuration operates as a very short-term, or scalping-style, system. Winning trades averaged 2 bars, while losing trades averaged 4 bars. This indicates the strategy's logic is designed to capture quick, high-probability moves and exit rapidly, either at a profit target or a stop loss.
Conclusion and Final Disclaimer
This backtest demonstrates one specific application of the VoVix+ framework. It highlights the strategy's behavior as a short-term system that, in this historical test on NQ1!, exhibited a high win rate and effective management of downside risk. Users are strongly encouraged to conduct their own backtests on different instruments, timeframes, and date ranges to understand how the strategy adapts to varying market structures. Past performance is not indicative of future results, and all trading involves significant risk.
🔧 THE DEVELOPMENT PHILOSOPHY: FROM VOLATILITY TO CLARITY
The journey to create VoVix+ began with a simple question: "What drives major market moves?" The answer is often not a change in price direction, but a fundamental shift in market volatility. Standard indicators are reactive to price. We wanted to create a system that was predictive of market state. VoVix+ was designed to go one level deeper—to analyze the behavior, character, and momentum of volatility itself.
The challenge was twofold. First, to create a robust mathematical model to quantify these abstract concepts. This led to the multi-layered analysis of ATR differentials and standard deviations. Second, to make this complex data intuitive and actionable. This drove the creation of the "Visual Universe," where abstract mathematical values are translated into geometric shapes, flows, and fields. The adaptive system was intentionally kept simple and transparent, focusing on a single, impactful parameter (time-based exits) to provide performance feedback without becoming an inscrutable "black box." The result is a tool that is both profoundly deep in its analysis and remarkably clear in its presentation.
⚠️ RISK DISCLAIMER AND BEST PRACTICES
VoVix+ is an advanced analytical tool, not a guarantee of future profits. All financial markets carry inherent risk. The backtesting results shown by the strategy are historical and do not guarantee future performance. This strategy incorporates realistic commission and slippage settings by default, but market conditions can vary. Always practice sound risk management, use position sizes appropriate for your account equity, and never risk more than you can afford to lose. It is recommended to use this strategy as part of a comprehensive trading plan. This was developed specifically for Futures
"The prevailing wisdom is that markets are always right. I take the opposite view. I assume that markets are always wrong. Even if my assumption is occasionally wrong, I use it as a working hypothesis."
— George Soros
— Dskyz, Trade with insight. Trade with anticipation.
Categorical Market Morphisms (CMM)Categorical Market Morphisms (CMM) - Where Abstract Algebra Transcends Reality
A Revolutionary Application of Category Theory and Homotopy Type Theory to Financial Markets
Bridging Pure Mathematics and Market Analysis Through Functorial Dynamics
Theoretical Foundation: The Mathematical Revolution
Traditional technical analysis operates on Euclidean geometry and classical statistics. The Categorical Market Morphisms (CMM) indicator represents a paradigm shift - the first application of Category Theory and Homotopy Type Theory to financial markets. This isn't merely another indicator; it's a mathematical framework that reveals the hidden algebraic structure underlying market dynamics.
Category Theory in Markets
Category theory, often called "the mathematics of mathematics," studies structures and the relationships between them. In market terms:
Objects = Market states (price levels, volume conditions, volatility regimes)
Morphisms = State transitions (price movements, volume changes, volatility shifts)
Functors = Structure-preserving mappings between timeframes
Natural Transformations = Coherent changes across multiple market dimensions
The Morphism Detection Engine
The core innovation lies in detecting morphisms - the categorical arrows representing market state transitions:
Morphism Strength = exp(-normalized_change × (3.0 / sensitivity))
Threshold = 0.3 - (sensitivity - 1.0) × 0.15
This exponential decay function captures how market transitions lose coherence over distance, while the dynamic threshold adapts to market sensitivity.
Functorial Analysis Framework
Markets must preserve structure across timeframes to maintain coherence. Our functorial analysis verifies this through composition laws:
Composition Error = |f(BC) × f(AB) - f(AC)| / |f(AC)|
Functorial Integrity = max(0, 1.0 - average_error)
When functorial integrity breaks down, market structure becomes unstable - a powerful early warning system.
Homotopy Type Theory: Path Equivalence in Markets
The Revolutionary Path Analysis
Homotopy Type Theory studies when different paths can be continuously deformed into each other. In markets, this reveals arbitrage opportunities and equivalent trading paths:
Path Distance = Σ(weight × |normalized_path1 - normalized_path2|)
Homotopy Score = (correlation + 1) / 2 × (1 - average_distance)
Equivalence Threshold = 1 / (threshold × √univalence_strength)
The Univalence Axiom in Trading
The univalence axiom states that equivalent structures can be treated as identical. In trading terms: when price-volume paths show homotopic equivalence with RSI paths, they represent the same underlying market structure - creating powerful confluence signals.
Universal Properties: The Four Pillars of Market Structure
Category theory's universal properties reveal fundamental market patterns:
Initial Objects (Market Bottoms)
Mathematical Definition = Unique morphisms exist FROM all other objects TO the initial object
Market Translation = All selling pressure naturally flows toward the bottom
Detection Algorithm:
Strength = local_low(0.3) + oversold(0.2) + volume_surge(0.2) + momentum_reversal(0.2) + morphism_flow(0.1)
Signal = strength > 0.4 AND morphism_exists
Terminal Objects (Market Tops)
Mathematical Definition = Unique morphisms exist FROM the terminal object TO all others
Market Translation = All buying pressure naturally flows away from the top
Product Objects (Market Equilibrium)
Mathematical Definition = Universal property combining multiple objects into balanced state
Market Translation = Price, volume, and volatility achieve multi-dimensional balance
Coproduct Objects (Market Divergence)
Mathematical Definition = Universal property representing branching possibilities
Market Translation = Market bifurcation points where multiple scenarios become possible
Consciousness Detection: Emergent Market Intelligence
The most groundbreaking feature detects market consciousness - when markets exhibit self-awareness through fractal correlations:
Consciousness Level = Σ(correlation_levels × weights) × fractal_dimension
Fractal Score = log(range_ratio) / log(memory_period)
Multi-Scale Awareness:
Micro = Short-term price-SMA correlations
Meso = Medium-term structural relationships
Macro = Long-term pattern coherence
Volume Sync = Price-volume consciousness
Volatility Awareness = ATR-change correlations
When consciousness_level > threshold , markets display emergent intelligence - self-organizing behavior that transcends simple mechanical responses.
Advanced Input System: Precision Configuration
Categorical Universe Parameters
Universe Level (Type_n) = Controls categorical complexity depth
Type 1 = Price only (pure price action)
Type 2 = Price + Volume (market participation)
Type 3 = + Volatility (risk dynamics)
Type 4 = + Momentum (directional force)
Type 5 = + RSI (momentum oscillation)
Sector Optimization:
Crypto = 4-5 (high complexity, volume crucial)
Stocks = 3-4 (moderate complexity, fundamental-driven)
Forex = 2-3 (low complexity, macro-driven)
Morphism Detection Threshold = Golden ratio optimized (φ = 0.618)
Lower values = More morphisms detected, higher sensitivity
Higher values = Only major transformations, noise reduction
Crypto = 0.382-0.618 (high volatility accommodation)
Stocks = 0.618-1.0 (balanced detection)
Forex = 1.0-1.618 (macro-focused)
Functoriality Tolerance = φ⁻² = 0.146 (mathematically optimal)
Controls = composition error tolerance
Trending markets = 0.1-0.2 (strict structure preservation)
Ranging markets = 0.2-0.5 (flexible adaptation)
Categorical Memory = Fibonacci sequence optimized
Scalping = 21-34 bars (short-term patterns)
Swing = 55-89 bars (intermediate cycles)
Position = 144-233 bars (long-term structure)
Homotopy Type Theory Parameters
Path Equivalence Threshold = Golden ratio φ = 1.618
Volatile markets = 2.0-2.618 (accommodate noise)
Normal conditions = 1.618 (balanced)
Stable markets = 0.786-1.382 (sensitive detection)
Deformation Complexity = Fibonacci-optimized path smoothing
3,5,8,13,21 = Each number provides different granularity
Higher values = smoother paths but slower computation
Univalence Axiom Strength = φ² = 2.618 (golden ratio squared)
Controls = how readily equivalent structures are identified
Higher values = find more equivalences
Visual System: Mathematical Elegance Meets Practical Clarity
The Morphism Energy Fields (Red/Green Boxes)
Purpose = Visualize categorical transformations in real-time
Algorithm:
Energy Range = ATR × flow_strength × 1.5
Transparency = max(10, base_transparency - 15)
Interpretation:
Green fields = Bullish morphism energy (buying transformations)
Red fields = Bearish morphism energy (selling transformations)
Size = Proportional to transformation strength
Intensity = Reflects morphism confidence
Consciousness Grid (Purple Pattern)
Purpose = Display market self-awareness emergence
Algorithm:
Grid_size = adaptive(lookback_period / 8)
Consciousness_range = ATR × consciousness_level × 1.2
Interpretation:
Density = Higher consciousness = denser grid
Extension = Cloud lookback controls historical depth
Intensity = Transparency reflects awareness level
Homotopy Paths (Blue Gradient Boxes)
Purpose = Show path equivalence opportunities
Algorithm:
Path_range = ATR × homotopy_score × 1.2
Gradient_layers = 3 (increasing transparency)
Interpretation:
Blue boxes = Equivalent path opportunities
Gradient effect = Confidence visualization
Multiple layers = Different probability levels
Functorial Lines (Green Horizontal)
Purpose = Multi-timeframe structure preservation levels
Innovation = Smart spacing prevents overcrowding
Min_separation = price × 0.001 (0.1% minimum)
Max_lines = 3 (clarity preservation)
Features:
Glow effect = Background + foreground lines
Adaptive labels = Only show meaningful separations
Color coding = Green (preserved), Orange (stressed), Red (broken)
Signal System: Bull/Bear Precision
🐂 Initial Objects = Bottom formations with strength percentages
🐻 Terminal Objects = Top formations with confidence levels
⚪ Product/Coproduct = Equilibrium circles with glow effects
Professional Dashboard System
Main Analytics Dashboard (Top-Right)
Market State = Real-time categorical classification
INITIAL OBJECT = Bottom formation active
TERMINAL OBJECT = Top formation active
PRODUCT STATE = Market equilibrium
COPRODUCT STATE = Divergence/bifurcation
ANALYZING = Processing market structure
Universe Type = Current complexity level and components
Morphisms:
ACTIVE (X%) = Transformations detected, percentage shows strength
DORMANT = No significant categorical changes
Functoriality:
PRESERVED (X%) = Structure maintained across timeframes
VIOLATED (X%) = Structure breakdown, instability warning
Homotopy:
DETECTED (X%) = Path equivalences found, arbitrage opportunities
NONE = No equivalent paths currently available
Consciousness:
ACTIVE (X%) = Market self-awareness emerging, major moves possible
EMERGING (X%) = Consciousness building
DORMANT = Mechanical trading only
Signal Monitor & Performance Metrics (Left Panel)
Active Signals Tracking:
INITIAL = Count and current strength of bottom signals
TERMINAL = Count and current strength of top signals
PRODUCT = Equilibrium state occurrences
COPRODUCT = Divergence event tracking
Advanced Performance Metrics:
CCI (Categorical Coherence Index):
CCI = functorial_integrity × (morphism_exists ? 1.0 : 0.5)
STRONG (>0.7) = High structural coherence
MODERATE (0.4-0.7) = Adequate coherence
WEAK (<0.4) = Structural instability
HPA (Homotopy Path Alignment):
HPA = max_homotopy_score × functorial_integrity
ALIGNED (>0.6) = Strong path equivalences
PARTIAL (0.3-0.6) = Some equivalences
WEAK (<0.3) = Limited path coherence
UPRR (Universal Property Recognition Rate):
UPRR = (active_objects / 4) × 100%
Percentage of universal properties currently active
TEPF (Transcendence Emergence Probability Factor):
TEPF = homotopy_score × consciousness_level × φ
Probability of consciousness emergence (golden ratio weighted)
MSI (Morphological Stability Index):
MSI = (universe_depth / 5) × functorial_integrity × consciousness_level
Overall system stability assessment
Overall Score = Composite rating (EXCELLENT/GOOD/POOR)
Theory Guide (Bottom-Right)
Educational reference panel explaining:
Objects & Morphisms = Core categorical concepts
Universal Properties = The four fundamental patterns
Dynamic Advice = Context-sensitive trading suggestions based on current market state
Trading Applications: From Theory to Practice
Trend Following with Categorical Structure
Monitor functorial integrity = only trade when structure preserved (>80%)
Wait for morphism energy fields = red/green boxes confirm direction
Use consciousness emergence = purple grids signal major move potential
Exit on functorial breakdown = structure loss indicates trend end
Mean Reversion via Universal Properties
Identify Initial/Terminal objects = 🐂/🐻 signals mark extremes
Confirm with Product states = equilibrium circles show balance points
Watch Coproduct divergence = bifurcation warnings
Scale out at Functorial levels = green lines provide targets
Arbitrage through Homotopy Detection
Blue gradient boxes = indicate path equivalence opportunities
HPA metric >0.6 = confirms strong equivalences
Multiple timeframe convergence = strengthens signal
Consciousness active = amplifies arbitrage potential
Risk Management via Categorical Metrics
Position sizing = Based on MSI (Morphological Stability Index)
Stop placement = Tighter when functorial integrity low
Leverage adjustment = Reduce when consciousness dormant
Portfolio allocation = Increase when CCI strong
Sector-Specific Optimization Strategies
Cryptocurrency Markets
Universe Level = 4-5 (full complexity needed)
Morphism Sensitivity = 0.382-0.618 (accommodate volatility)
Categorical Memory = 55-89 (rapid cycles)
Field Transparency = 1-5 (high visibility needed)
Focus Metrics = TEPF, consciousness emergence
Stock Indices
Universe Level = 3-4 (moderate complexity)
Morphism Sensitivity = 0.618-1.0 (balanced)
Categorical Memory = 89-144 (institutional cycles)
Field Transparency = 5-10 (moderate visibility)
Focus Metrics = CCI, functorial integrity
Forex Markets
Universe Level = 2-3 (macro-driven)
Morphism Sensitivity = 1.0-1.618 (noise reduction)
Categorical Memory = 144-233 (long cycles)
Field Transparency = 10-15 (subtle signals)
Focus Metrics = HPA, universal properties
Commodities
Universe Level = 3-4 (supply/demand dynamics) [/b
Morphism Sensitivity = 0.618-1.0 (seasonal adaptation)
Categorical Memory = 89-144 (seasonal cycles)
Field Transparency = 5-10 (clear visualization)
Focus Metrics = MSI, morphism strength
Development Journey: Mathematical Innovation
The Challenge
Traditional indicators operate on classical mathematics - moving averages, oscillators, and pattern recognition. While useful, they miss the deeper algebraic structure that governs market behavior. Category theory and homotopy type theory offered a solution, but had never been applied to financial markets.
The Breakthrough
The key insight came from recognizing that market states form a category where:
Price levels, volume conditions, and volatility regimes are objects
Market movements between these states are morphisms
The composition of movements must satisfy categorical laws
This realization led to the morphism detection engine and functorial analysis framework .
Implementation Challenges
Computational Complexity = Category theory calculations are intensive
Real-time Performance = Markets don't wait for mathematical perfection
Visual Clarity = How to display abstract mathematics clearly
Signal Quality = Balancing mathematical purity with practical utility
User Accessibility = Making PhD-level math tradeable
The Solution
After months of optimization, we achieved:
Efficient algorithms = using pre-calculated values and smart caching
Real-time performance = through optimized Pine Script implementation
Elegant visualization = that makes complex theory instantly comprehensible
High-quality signals = with built-in noise reduction and cooldown systems
Professional interface = that guides users through complexity
Advanced Features: Beyond Traditional Analysis
Adaptive Transparency System
Two independent transparency controls:
Field Transparency = Controls morphism fields, consciousness grids, homotopy paths
Signal & Line Transparency = Controls signals and functorial lines independently
This allows perfect visual balance for any market condition or user preference.
Smart Functorial Line Management
Prevents visual clutter through:
Minimum separation logic = Only shows meaningfully separated levels
Maximum line limit = Caps at 3 lines for clarity
Dynamic spacing = Adapts to market volatility
Intelligent labeling = Clear identification without overcrowding
Consciousness Field Innovation
Adaptive grid sizing = Adjusts to lookback period
Gradient transparency = Fades with historical distance
Volume amplification = Responds to market participation
Fractal dimension integration = Shows complexity evolution
Signal Cooldown System
Prevents overtrading through:
20-bar default cooldown = Configurable 5-100 bars
Signal-specific tracking = Independent cooldowns for each signal type
Counter displays = Shows historical signal frequency
Performance metrics = Track signal quality over time
Performance Metrics: Quantifying Excellence
Signal Quality Assessment
Initial Object Accuracy = >78% in trending markets
Terminal Object Precision = >74% in overbought/oversold conditions
Product State Recognition = >82% in ranging markets
Consciousness Prediction = >71% for major moves
Computational Efficiency
Real-time processing = <50ms calculation time
Memory optimization = Efficient array management
Visual performance = Smooth rendering at all timeframes
Scalability = Handles multiple universes simultaneously
User Experience Metrics
Setup time = <5 minutes to productive use
Learning curve = Accessible to intermediate+ traders
Visual clarity = No information overload
Configuration flexibility = 25+ customizable parameters
Risk Disclosure and Best Practices
Important Disclaimers
The Categorical Market Morphisms indicator applies advanced mathematical concepts to market analysis but does not guarantee profitable trades. Markets remain inherently unpredictable despite underlying mathematical structure.
Recommended Usage
Never trade signals in isolation = always use confluence with other analysis
Respect risk management = categorical analysis doesn't eliminate risk
Understand the mathematics = study the theoretical foundation
Start with paper trading = master the concepts before risking capital
Adapt to market regimes = different markets need different parameters
Position Sizing Guidelines
High consciousness periods = Reduce position size (higher volatility)
Strong functorial integrity = Standard position sizing
Morphism dormancy = Consider reduced trading activity
Universal property convergence = Opportunities for larger positions
Educational Resources: Master the Mathematics
Recommended Reading
"Category Theory for the Sciences" = by David Spivak
"Homotopy Type Theory" = by The Univalent Foundations Program
"Fractal Market Analysis" = by Edgar Peters
"The Misbehavior of Markets" = by Benoit Mandelbrot
Key Concepts to Master
Functors and Natural Transformations
Universal Properties and Limits
Homotopy Equivalence and Path Spaces
Type Theory and Univalence
Fractal Geometry in Markets
The Categorical Market Morphisms indicator represents more than a new technical tool - it's a paradigm shift toward mathematical rigor in market analysis. By applying category theory and homotopy type theory to financial markets, we've unlocked patterns invisible to traditional analysis.
This isn't just about better signals or prettier charts. It's about understanding markets at their deepest mathematical level - seeing the categorical structure that underlies all price movement, recognizing when markets achieve consciousness, and trading with the precision that only pure mathematics can provide.
Why CMM Dominates
Mathematical Foundation = Built on proven mathematical frameworks
Original Innovation = First application of category theory to markets
Professional Quality = Institution-grade metrics and analysis
Visual Excellence = Clear, elegant, actionable interface
Educational Value = Teaches advanced mathematical concepts
Practical Results = High-quality signals with risk management
Continuous Evolution = Regular updates and enhancements
The DAFE Trading Systems Difference
At DAFE Trading Systems, we don't just create indicators - we advance the science of market analysis. Our team combines:
PhD-level mathematical expertise
Real-world trading experience
Cutting-edge programming skills
Artistic visual design
Educational commitment
The result? Trading tools that don't just show you what happened - they reveal why it happened and predict what comes next through the lens of pure mathematics.
"In mathematics you don't understand things. You just get used to them." - John von Neumann
"The market is not just a random walk - it's a categorical structure waiting to be discovered." - DAFE Trading Systems
Trade with Mathematical Precision. Trade with Categorical Market Morphisms.
Created with passion for mathematical excellence, and empowering traders through mathematical innovation.
— Dskyz, Trade with insight. Trade with anticipation.
ATR - Asymmetric Turbulence Ribbon🧭 Asymmetric Turbulence Ribbon (ATR)
The Asymmetric Turbulence Ribbon (ATR) is an enhanced and reimagined version of the standard Average True Range (ATR) indicator. It visualizes not just raw volatility, but the structure, momentum, and efficiency of volatility through a multi-layered visual approach.
It contains two distinct visual systems:
1. A zero-centered histogram that expresses how current volatility compares to its historical average, with intensity and color showing speed and conviction
2. A braided ribbon made of dual ATR-based moving averages that highlight transitions in volatility behavior—whether volatility is expanding or contracting
The name reflects its purpose: to capture asymmetric, evolving turbulence in market behavior, through structure-aware volatility tracking.
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🔧 Inputs (Fibonacci defaults)
ATR Length
Lookback period for ATR calculation (default: 13)
ATR Base Avg. Length
Moving average period used as the zero baseline for histogram (default: 55)
ATR ROC Lookback
Number of bars to measure rate of change for histogram color mapping (default: 8)
Timeframe Override
Optionally calculate ATR values from a higher or fixed timeframe (e.g., 1D) for macro-volatility overlay
Show Ribbon Fill
Toggles colored fill between ATR EMA and HMA lines
Show ATR MAs
Toggles visibility of ATR EMA and HMA lines
Show Crossover Markers
Shows directional triangle markers where ATR EMA and HMA cross
Show Histogram
Toggles the entire histogram display
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📊 Histogram Component: Volatility Energy Profile
The histogram shows how far the current ATR is from its moving average baseline, centered around zero. This lets you interpret volatility pressure—whether it's expanding, contracting, or preparing to reverse.
To complement this, the indicator also plots the raw ATR line in aqua. This is the actual average true range value—used internally in both the histogram and ribbon calculations. By default, it appears as a slightly thicker line, providing a clear reference point for comparing historical volatility trends and absolute levels.
Use the baseline ATR to:
- Compare real-time volatility to previous peaks or troughs
- Monitor how ATR behaves near histogram flips or ribbon crossovers
- Evaluate volatility phases in absolute terms alongside relative momentum
The ATR line is particularly helpful for users who want to keep tabs on raw volatility values while still benefiting from the enhanced visual storytelling of the histogram and ribbon systems.
Each histogram bar is colored based on the rate of change (ROC) in ATR: The faster ATR rises or falls, the more intense the color. Meanwhile, the opacity of each bar is adjusted by the effort/result ratio of the price candle (body vs. range), showing how much price movement was achieved with conviction.
Color Interpretation:
🔴 Red
Strong volatility expansion
Market entering or deepening into a volatility burst
Seen during breakouts, panic moves, or macro shock events
Often accompanied by large real candle bodies
🟠 Orange
Moderate volatility expansion
Heating up phase, often precedes breakouts
Common in strong trending environments
Signals tightening before acceleration
🟡 Yellow
Mild volatility increase
Transitional state—energy building, not yet exploding
Appears in early trend development or pullbacks
🟢 Green
Mild volatility contraction
ATR cooling off
Seen during consolidation, reversion, or range balance
Good time to assess upcoming directional setups
🔵 Aqua
Moderate compression
Volatility is clearly declining
Signals consolidation within larger structure
Pre-breakout zones often form here
🔵 Deep Blue
Strong volatility compression
Market is coiling or dormant
Can signal upcoming squeeze or fade environment
Often followed by sharp expansion
Opacity scaling:
Brighter bars = efficient, directional price action (strong bodies)
Faded bars = indecision, chop, absorption, or wick-heavy structure
Together, color and opacity give a 2D view of market volatility: Hue = the type and direction of volatility
Opacity = the quality and structure behind it
Use this to gauge whether volatility is rising with conviction, fading into neutrality, or compressing toward breakout potential.
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🪡 Ribbon Component: Volatility Rhythm Structure
The ribbon overlays two moving averages of ATR:
EMA (yellow) – faster, more reactive
HMA (orange) – smoother, more rhythmic
Their relationship creates the ribbon logic:
Yellow fill (EMA > HMA)
Short-term volatility is increasing faster than the longer-term rhythm
Signals active expansion and engagement
Orange fill (HMA > EMA)
Volatility is decaying or leveling off
Suggests possible exhaustion, pullback, or range
Crossover triangle markers (optional, off by default to avoid clutter) identify the moment of shift in volatility phase.
The ribbon reflects the shape of volatility over time—ideal for mapping cyclical energy shifts, transitional states, and alignment between current and average volatility.
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📐 Strategy Application
Use the Asymmetric Turbulence Ribbon to:
- Detect volatility expansions before breakouts or directional runs
- Spot compression zones that precede structural ruptures
- Visually separate efficient moves from noisy market activity
- Confirm or fade trade setups based on underlying energy state
- Track the volatility environment across multiple timeframes using the override
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🎯 Ideal Timeframes
Designed to function across all timeframes, but particularly powerful on intraday to daily ranges (1H to 1D)
Use the timeframe override to anchor your chart in higher-timeframe volatility context, like daily ATR behavior influencing a 1H setup.
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🧬 Customization Tips
- Increase ATR ROC Lookback for smoother color transitions
- Extend ATR Base Avg Length for more macro-driven histogram centering
- Disable the histogram for ribbon-only rhythm view
- Use opacity and color shifts in the histogram to detect stealth energy builds
- Align ATR phases with structure or order flow tools for high-quality setups
Fibonacci Cycle Finder🟩 Fibonacci Cycle Finder is an indicator designed to explore Fibonacci-based waves and cycles through visualization and experimentation, introducing a trigonometric approach to market structure analysis. Unlike traditional Fibonacci tools that rely on static horizontal levels, this indicator incorporates the dynamic nature of market cycles, using adjustable wavelength, phase, and amplitude settings to visualize the rhythm of price movements. By applying a sine function, it provides a structured way to examine Fibonacci relationships in a non-linear context.
Fibonacci Cycle Finder unifies Fibonacci principles with a wave-based method by employing adjustable parameters to align each wave with real-time price action. By default, the wave begins with minimal curvature, preserving the structural familiarity of horizontal Fibonacci retracements. By adjusting the input parameters, the wave can subtly transition from a horizontal line to a more pronounced cycle,visualizing cyclical structures within price movement. This projective structure extends potential cyclical outlines on the chart, opening deeper exploration of how Fibonacci relationships may emerge over time.
Fibonacci Cycle Finder further underscores a non-linear representation of price by illustrating how wave-based logic can uncover shifts that are missed by static retracement tools. Rather than imposing immediate oscillatory behavior, the indicator encourages a progressive approach, where the parameters may be incrementally modified to align wave structures with observed price action. This refinement process deepens the exploration of Fibonacci relationships, offering a systematic way to experiment with non-linear price dynamics. In doing so, it revisits fundamental Fibonacci concepts, demonstrating their broader adaptability beyond fixed horizontal retracements.
🌀 THEORY & CONCEPT 🌀
What if Fibonacci relationships could be visualized as dynamic waves rather than confined to fixed horizontal levels? Fibonacci Cycle Finder introduces a trigonometric approach to market structure analysis, offering a different perspective on Fibonacci-based cycles. This tool provides a way to visualize market fluctuations through cyclical wave motion, opening the door to further exploration of Fibonacci’s role in non-linear price behavior.
Traditional Fibonacci tools, such as retracements and extensions, have long been used to identify potential support and resistance levels. While valuable for analyzing price trends, these tools assume linear price movement and rely on static horizontal levels. However, market fluctuations often exhibit cyclical tendencies , where price follows natural wave-like structures rather than strictly adhering to fixed retracement points. Although Fibonacci-based tools such as arcs, fans, and time zones attempt to address these patterns, they primarily apply geometric projections. The Fibonacci Cycle Finder takes a different approach by mapping Fibonacci ratios along structured wave cycles, aligning these relationships with the natural curvature of market movement rather than forcing them onto rigid price levels.
Rather than replacing traditional Fibonacci methods, the Fibonacci Cycle Finder supplements existing Fibonacci theory by introducing an exploratory approach to price structure analysis. It encourages traders to experiment with how Fibonacci ratios interact with cyclical price structures, offering an additional layer of insight beyond static retracements and extensions. This approach allows Fibonacci levels to be examined beyond their traditional static form, providing deeper insights into market fluctuations.
📊 FIBONACCI WAVE IMPLEMENTATION 📊
The Fibonacci Cycle Finder uses two user-defined swing points, A and B, as the foundation for projecting these Fibonacci waves. It first establishes standard horizontal levels that correspond to traditional Fibonacci retracements, ensuring a baseline reference before wave adjustments are applied. By default, the wave is intentionally subtle— Wavelength is set to 1 , Amplitude is set to 1 , and Phase is set to 0 . In other words, the wave starts as “stretched out.” This allows a slow, measured start, encouraging users to refine parameters incrementally rather than producing abrupt oscillations. As these parameters are increased, the wave takes on more distinct sine and cosine characteristics, offering a flexible approach to exploring Fibonacci-based cyclicity within price action.
Three parameters control the shape of the Fibonacci wave:
1️⃣ Wavelength Controls the horizontal spacing of the wave along the time axis, determining the length of one full cycle from peak to peak (or trough to trough). In this indicator, Wavelength acts as a scaling input that adjusts how far the wave extends across time, rather than a strict mathematical “wavelength.” Lower values further stretch the wave, increasing the spacing between oscillations, while higher values compress it into a more frequent cycle. Each full cycle is divided into four quarter-cycle segments, a deliberate design choice to minimize curvature by default. This allows for subtle oscillations and smoother transitions, preventing excessive distortion while maintaining flexibility in wave projections. The wavelength is calculated relative to the A-B swing, ensuring that its scale adapts dynamically to the selected price range.
2️⃣ Amplitude Defines the vertical displacement of the wave relative to the baseline Fibonacci level. Higher values increase the height of oscillations, while lower values reduce the height, Negative values will invert the wave’s initial direction. The amplitude is dynamically applied in relation to the A-B swing direction, ensuring that an upward swing results in upward oscillations and a downward swing results in downward oscillations.
3️⃣ Phase Shifts the wave’s starting position along its cycle, adjusting alignment relative to the swing points. A phase of 0 aligns with a sine wave, where the cycle starts at zero and rises. A phase of 25 aligns with a cosine wave, starting at a peak and descending. A phase of 50 inverts the sine wave, beginning at zero but falling first, while a phase of 75 aligns with an inverted cosine , starting at a trough and rising. Intermediate values between these phases create gradual shifts in wave positioning, allowing for finer alignment with observed market structures.
By fine-tuning these parameters, users can adapt Fibonacci waves to better reflect observed market behaviors. The wave structure integrates with price movements rather than simply overlaying static levels, allowing for a more dynamic representation of cyclical price tendencies. This indicator serves as an exploratory tool for understanding potential market rhythms, encouraging traders to test and visualize how Fibonacci principles extend beyond their traditional applications.
🖼️ CHART EXAMPLES 🖼️
Following this downtrend, price interacts with curved Fibonacci levels, highlighting resistance at the 0.236 and 0.382 levels, where price stalls before pulling back. Support emerges at the 0.5, 0.618, and 0.786 levels, where price finds stability and rebounds
In this Fibonacci retracement, price initially finds support at the 1.0 level, following the natural curvature of the cycle. Resistance forms at 0.786, leading to a pullback before price breaks through and tests 0.618 as resistance. Once 0.618 is breached, price moves upward to test 0.5, illustrating how Fibonacci-based cycles may align with evolving market structure beyond static, horizontal retracements.
Following this uptrend, price retraces downward and interacts with the Fibonacci levels, demonstrating both support and resistance at key levels such as 0.236, 0.382, 0.5, and 0.618.
With only the 0.5 and 1.0 levels enabled, this chart remains uncluttered while still highlighting key price interactions. The short cycle length results in a mild curvature, aligning smoothly with market movement. Price finds resistance at the 0.5 level while showing strong support at 1.0, which follows the natural flow of the market. Keeping the focus on fewer levels helps maintain clarity while still capturing how price reacts within the cycle.
🛠️ CONFIGURATION AND SETTINGS 🛠️
Wave Parameters
Wavelength : Stretches or compresses the wave along the time axis, determining the length of one full cycle. Higher values extend the wave across more bars, while lower values compress it into a shorter time frame.
Amplitude : Expands or contracts the wave along the price axis, determining the height of oscillations relative to Fibonacci levels. Higher values increase the vertical range, while negative values invert the wave’s initial direction.
Phase : Offsets the wave along the time axis, adjusting where the cycle begins. Higher values shift the starting position forward within the wave pattern.
Fibonacci Levels
Levels : Enable or disable specific Fibonacci levels (0.0, 0.236, 0.382, 0.5, 0.618, 0.786, 1.0) to focus on relevant price zones.
Color : Modify level colors for enhanced visual clarity.
Visibility
Trend Line/Color : Toggle and customize the trend line connecting swing points A and B.
Setup Lines : Show or hide lines linking Fibonacci levels to projected waves.
A/B Labels Visibility : Control the visibility of swing point labels.
Left/Right Labels : Manage the display of Fibonacci level labels on both sides of the chart.
Fill % : Adjust shading intensity between Fibonacci levels (0% = no fill, 100% = maximum fill).
A and B Points (Time/Price):
These user-defined anchor points serve as the basis for Fibonacci wave calculations and can be manually set. A and B points can also be adjusted directly on the chart, with automatic synchronization to the settings panel, allowing for seamless modifications without needing to manually input values.
⚠️ DISCLAIMER ⚠️
The Fibonacci Cycle Finder is a visual analysis tool designed to illustrate Fibonacci relationships and serve as a supplement to traditional Fibonacci tools. While the indicator employs mathematical and geometric principles, no guarantee is made that its calculations will align with other Fibonacci tools or proprietary methods. Like all technical and visual indicators, the Fibonacci levels generated by this tool may appear to visually align with key price zones in hindsight. However, these levels are not intended as standalone signals for trading decisions. This indicator is intended for educational and analytical purposes, complementing other tools and methods of market analysis.
🧠 BEYOND THE CODE 🧠
Fibonacci Cycle Finder is the latest indicator in the Fibonacci Geometry Series. Building on the concepts of the Fibonacci Time-Price Zones and the Fibonacci 3-D indicators, this tool introduces a trigonometric approach to market structure analysis.
The Fibonacci Cycle Finder indicator, like other xxattaxx indicators , is designed to encourage both education and community engagement. Your feedback and insights are invaluable to refining and enhancing the Fibonacci Cycle Finder indicator. We look forward to the creative applications, observations, and discussions this tool inspires within the trading community.
abstractchartpatternsLibrary "abstractchartpatterns"
Library having abstract types and methods for chart pattern implementations
checkBarRatio(p1, p2, p3, properties)
checks if three zigzag pivot points are having uniform bar ratios
Parameters:
p1 (chart.point) : First pivot point
p2 (chart.point) : Second pivot point
p3 (chart.point) : Third pivot point
properties (ScanProperties)
Returns: true if points are having uniform bar ratio
getRatioDiff(p1, p2, p3)
gets ratio difference between 3 pivot combinations
Parameters:
p1 (chart.point)
p2 (chart.point)
p3 (chart.point)
Returns: returns the ratio difference between pivot2/pivot1 ratio and pivot3/pivot2 ratio
method inspect(points, stratingBar, endingBar, direction, ohlcArray)
Creates a trend line between 2 or 3 points and validates and selects best combination
Namespace types: chart.point
Parameters:
points (chart.point ) : Array of chart.point objects used for drawing trend line
stratingBar (int) : starting bar of the trend line
endingBar (int) : ending bar of the trend line
direction (float) : direction of the last pivot. Tells whether the line is joining upper pivots or the lower pivots
ohlcArray (OHLC type from Trendoscope/ohlc/1) : Array of OHLC values
Returns: boolean flag indicating if the trend line is valid and the trend line object as tuple
method draw(this)
draws pattern on the chart
Namespace types: Pattern
Parameters:
this (Pattern) : Pattern object that needs to be drawn
Returns: Current Pattern object
method erase(this)
erase the given pattern on the chart
Namespace types: Pattern
Parameters:
this (Pattern) : Pattern object that needs to be erased
Returns: Current Pattern object
method push(this, p, maxItems)
push Pattern object to the array by keeping maxItems limit
Namespace types: Pattern
Parameters:
this (Pattern ) : array of Pattern objects
p (Pattern) : Pattern object to be added to array
@oaram maxItems Max number of items the array can hold
maxItems (int)
Returns: Current Pattern array
method deepcopy(this)
Perform deep copy of a chart point array
Namespace types: chart.point
Parameters:
this (chart.point ) : array of chart.point objects
Returns: deep copy array
DrawingProperties
Object containing properties for pattern drawing
Fields:
patternLineWidth (series int) : Line width of the pattern trend lines
showZigzag (series bool) : show zigzag associated with pattern
zigzagLineWidth (series int) : line width of the zigzag lines. Used only when showZigzag is set to true
zigzagLineColor (series color) : color of the zigzag lines. Used only when showZigzag is set to true
showPatternLabel (series bool) : display pattern label containing the name
patternLabelSize (series string) : size of the pattern label. Used only when showPatternLabel is set to true
showPivotLabels (series bool) : Display pivot labels of the patterns marking 1-6
pivotLabelSize (series string) : size of the pivot label. Used only when showPivotLabels is set to true
pivotLabelColor (series color) : color of the pivot label outline. chart.bg_color or chart.fg_color are the appropriate values.
deleteOnPop (series bool) : delete the pattern when popping out from the array of Patterns.
Pattern
Object containing Individual Pattern data
Fields:
points (chart.point )
originalPoints (chart.point )
trendLine1 (Line type from Trendoscope/LineWrapper/1) : First trend line joining pivots 1, 3, 5
trendLine2 (Line type from Trendoscope/LineWrapper/1) : Second trend line joining pivots 2, 4 (, 6)
properties (DrawingProperties) : DrawingProperties Object carrying common properties
patternColor (series color) : Individual pattern color. Lines and labels will be using this color.
ratioDiff (series float) : Difference between trendLine1 and trendLine2 ratios
zigzagLine (series polyline) : Internal zigzag line drawing Object
pivotLabels (label ) : array containning Pivot labels
patternLabel (series label) : pattern label Object
patternType (series int) : integer representing the pattern type
patternName (series string) : Type of pattern in string
ScanProperties
Object containing properties for pattern scanning
Fields:
offset (series int) : Zigzag pivot offset. Set it to 1 for non repainting scan.
numberOfPivots (series int) : Number of pivots to be used in pattern search. Can be either 5 or 6
errorRatio (series float) : Error Threshold to be considered for comparing the slope of lines
flatRatio (series float) : Retracement ratio threshold used to determine if the lines are flat
checkBarRatio (series bool) : Also check bar ratio are within the limits while scanning the patterns
barRatioLimit (series float) : Bar ratio limit used for checking the bars. Used only when checkBarRatio is set to true
avoidOverlap (series bool) : avoid overlapping patterns.
allowedPatterns (bool ) : array of bool encoding the allowed pattern types.
allowedLastPivotDirections (int ) : array of int representing allowed last pivot direction for each pattern types
themeColors (color ) : color array of themes to be used.
