Volume Weighted Correlation

This indicator analyzes the structural relationship between two
assets by decomposing the Total Correlation into two distinct,
interpretable components: "Between-Bar" (Inter-Bar) and
"Within-Bar" (Intra-Bar) correlation.

Key Features:

1. **Hybrid Copula Estimator:** Unlike standard correlation, which
often fails on High/Low range data, this indicator fuses two
metrics to ensure mathematical rigor:
- **Magnitude:** Derived from Rogers-Satchell Volatility.
- **Direction:** Derived from Log-Returns.
This allows for precise correlation estimates even on intra-bar data.

2. **Two-Component Correlation Decomposition:** The indicator
separates correlation based on the 'Estimate Bar Statistics' option.
- **Standard Mode (`Estimate Bar Statistics` = OFF):** Calculates
correlation based on the selected `Source` (Close-to-Close).
- **Decomposition Mode (`Estimate Bar Statistics` = ON):** The
indicator uses a statistical model ('Estimator') to
calculate *within-bar* correlation.
This separates the relationship into:
- **Between-Bar Correlation (Green/Red):** Correlation of the
price paths (means). Indicates if the macro movements of the
assets are aligned (Inter-Bar correlation).
- **Within-Bar Correlation (Blue):** Correlation of the
microstructure (Intra-Bar volatility/noise).

3. **Visual Decomposition Logic:** Total Correlation is the
primary metric displayed. Since Correlation Coefficients are not
linearly additive, this indicator calculates the *exact* Total
Correlation and partitions the area/ratios based on the additive
Covariance Decomposition (`CovTot = CovBtw + CovWtn`). This
ensures the displayed total correlation remains mathematically accurate.

4. **Dual Display Modes:** The indicator offers two modes to
visualize this decomposition:
- **Absolute Mode:** Displays the *Total Correlation* as the main
line, with the background filled by the stacked components
(Between vs. Within). Shows the *magnitude* of the relationship.
- **Relative Mode:** Displays the **Energy Ratios** (-1.0 to 1.0)
of each component using L1-Normalization. This isolates the
*structure/quality* of the relationship (e.g., "Is the correlation
driven by price movement or just by volatility coupling?").

5. **Calculation Options:**
- **Normalization:** An optional 'Normalize' setting
calculates an **Exponential Regression Curve** (log-space),
creating a constant percentage variance environment. Essential
for comparing assets with different scales (e.g., BTC vs EURUSD).
- **Volume Weighting:** An option (`Volume weighted`) applies
volume weighting to all mean and covariance calculations.

6. **Correlation Cycle Analysis:**
- **Pivot Detection:** Includes a built-in pivot detector
that identifies significant turning points (highs and lows) in
the *Total Correlation* line. (Note: This is only visible
in 'Absolute Mode').
- **Flexible Pivot Algorithms:** Supports various underlying
mathematical models for pivot detection provided by the
core library.

7. **Note on Confirmation (Lag):** Pivot signals are confirmed
using a lookback method. A pivot is only plotted *after*
the `Pivot Right Bars` input has passed, which introduces
an inherent lag.

8. **Multi-Timeframe (MTF) Capability:**
- **MTF Correlation Lines:** The correlation lines can be
calculated on a higher timeframe, with standard options
to handle gaps (`Fill Gaps`) and prevent repainting
(`Wait for...`).
- **Limitation:** The Pivot detection (`Calculate Pivots`) is
**disabled** if a Higher Timeframe (HTF) is selected.

9. **Integrated Alerts:** Includes comprehensive alerts for:
- Correlation magnitude (High Positive / High Inverse).
- Character changes (Inter-Bar vs. Intra-Bar dominance).
- Total Correlation pivot (High/Low) detection.

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**DISCLAIMER**

1. **For Informational/Educational Use Only:** This indicator is
provided for informational and educational purposes only. It does
not constitute financial, investment, or trading advice, nor is
it a recommendation to buy or sell any asset.

2. **Use at Your Own Risk:** All trading decisions you make based on
the information or signals generated by this indicator are made
solely at your own risk.

3. **No Guarantee of Performance:** Past performance is not an
indicator of future results. The author makes no guarantee
regarding the accuracy of the signals or future profitability.

4. **No Liability:** The author shall not be held liable for any
financial losses or damages incurred directly or indirectly from
the use of this indicator.

5. **Signals Are Not Recommendations:** The alerts and visual signals
(e.g., crossovers) generated by this tool are not direct
recommendations to buy or sell. They are technical observations
for your own analysis and consideration.