Fast Autocorrelation Estimator

█ Overview:
The Fast ACF and PACF Estimation indicator efficiently calculates the autocorrelation function (ACF) and partial autocorrelation function (PACF) using an online implementation. It helps traders identify patterns and relationships in financial time series data, enabling them to optimize their trading strategies and make better-informed decisions in the markets.

█ Concepts:
Autocorrelation, also known as serial correlation, is the correlation of a signal with a delayed copy of itself as a function of delay.

This indicator displays autocorrelation based on lag number. The autocorrelation is not displayed based over time on the x-axis. It's based on the lag number which ranges from 1 to 30. The calculations can be done with "Log Returns", "Absolute Log Returns" or "Original Source" (the price of the asset displayed on the chart).

When calculating autocorrelation, the resulting value will range from +1 to -1, in line with the traditional correlation statistic. An autocorrelation of +1 represents a perfect correlation (an increase seen in one time series leads to a proportionate increase in the other time series). An autocorrelation of -1, on the other hand, represents a perfect inverse correlation (an increase seen in one time series results in a proportionate decrease in the other time series). Lag number indicates which historical data point is autocorrelated. For example, if lag 3 shows significant autocorrelation, it means current data is influenced by the data three bars ago.

The Fast Online Estimation of ACF and PACF Indicator is a powerful tool for analyzing the linear relationship between a time series and its lagged values in TradingView. The indicator implements an online estimation of the Autocorrelation Function (ACF) and the Partial Autocorrelation Function (PACF) up to 30 lags, providing a real-time assessment of the underlying dependencies in your time series data. The Autocorrelation Function (ACF) measures the linear relationship between a time series and its lagged values, capturing both direct and indirect dependencies. The Partial Autocorrelation Function (PACF) isolates the direct dependency between the time series and a specific lag while removing the effect of any indirect dependencies.

This distinction is crucial in understanding the underlying relationships in time series data and making more informed decisions based on those relationships. For example, let's consider a time series with three variables: A, B, and C. Suppose that A has a direct relationship with B, B has a direct relationship with C, but A and C do not have a direct relationship. The ACF between A and C will capture the indirect relationship between them through B, while the PACF will show no significant relationship between A and C, as it accounts for the indirect dependency through B. Meaning that when ACF is significant at for lag 5, the dependency detected could be caused by an observation that came in between, and PACF accounts for that. This indicator leverages the Fast Moments algorithm to efficiently calculate autocorrelations, making it ideal for analyzing large datasets or real-time data streams. By using the Fast Moments algorithm, the indicator can quickly update ACF and PACF values as new data points arrive, reducing the computational load and ensuring timely analysis. The PACF is derived from the ACF using the Durbin-Levinson algorithm, which helps in isolating the direct dependency between a time series and its lagged values, excluding the influence of other intermediate lags.

█ How to Use the Indicator:

Interpreting autocorrelation values can provide valuable insights into the market behavior and potential trading strategies.

When applying autocorrelation to log returns, and a specific lag shows a high positive autocorrelation, it suggests that the time series tends to move in the same direction over that lag period. In this case, a trader might consider using a momentum-based strategy to capitalize on the continuation of the current trend. On the other hand, if a specific lag shows a high negative autocorrelation, it indicates that the time series tends to reverse its direction over that lag period. In this situation, a trader might consider using a mean-reversion strategy to take advantage of the expected reversal in the market.

ACF of log returns:

Absolute returns are often used to as a measure of volatility. There is usually significant positive autocorrelation in absolute returns. We will often see an exponential decay of autocorrelation in volatility. This means that current volatility is dependent on historical volatility and the effect slowly dies off as the lag increases. This effect shows the property of "volatility clustering". Which means large changes tend to be followed by large changes, of either sign, and small changes tend to be followed by small changes.

ACF of absolute log returns:

Autocorrelation in price is always significantly positive and has an exponential decay. This predictably positive and relatively large value makes the autocorrelation of price (not returns) generally less useful.

ACF of price:


█ Significance:



The significance of a correlation metric tells us whether we should pay attention to it. In this script, we use 95% confidence interval bands that adjust to the size of the sample. If the observed correlation at a specific lag falls within the confidence interval, we consider it not significant and the data to be random or IID (identically and independently distributed). This means that we can't confidently say that the correlation reflects a real relationship, rather than just random chance. However, if the correlation is outside of the confidence interval, we can state with 95% confidence that there is an association between the lagged values. In other words, the correlation is likely to reflect a meaningful relationship between the variables, rather than a coincidence. A significant difference in either ACF or PACF can provide insights into the underlying structure of the time series data and suggest potential strategies for traders. By understanding these complex patterns, traders can better tailor their strategies to capitalize on the observed dependencies in the data, which can lead to improved decision-making in the financial markets.

Significant ACF but not significant PACF: This might indicate the presence of a moving average (MA) component in the time series. A moving average component is a pattern where the current value of the time series is influenced by a weighted average of past values. In this case, the ACF would show significant correlations over several lags, while the PACF would show significance only at the first few lags and then quickly decay.

Significant PACF but not significant ACF: This might indicate the presence of an autoregressive (AR) component in the time series. An autoregressive component is a pattern where the current value of the time series is influenced by a linear combination of past values at specific lags.

Often we find both significant ACF and PACF, in that scenario simply and AR or MA model might not be sufficient and a more complex model such as ARMA or ARIMA can be used.

█ Features:
Source selection: User can choose either 'Log Returns' , 'Absolute Returns' or 'Original Source' for the input data.
Autocorrelation Selection: User can choose either 'ACF' or 'PACF' for the plot selection.
Plot Selection: User can choose either 'Autocorrelarrogram' or 'Historical Autocorrelation' for plotting the historical autocorrelation at a specified lag.
Max Lag: User can select the maximum number of lags to plot.
Precision: User can set the number of decimal points to display in the plot.