Momentum Regression

The Momentum Regression indicator provides a robust statistical framework for analyzing momentum effects in financial markets by leveraging volatility-adjusted linear regression. It helps traders identify if momentum is statistically significant and tradable, providing visual deviation bands and a comprehensive data summary to assist in regime detection and strategy validation.

Usage

The Momentum Regression tool is used as a quantitative filter to verify market regimes. Traders can use it to determine if an asset is exhibiting continuation (positive slope) or reversion (negative slope) characteristics.

• Trend Identification: A positive slope indicates a momentum-following environment, while a negative slope suggests a mean-reverting environment.
• Overextended Markets: The deviation bands (standard deviations of residuals) highlight areas where price action has moved significantly away from the regression trendline, acting as dynamic overbought or oversold zones.
• Statistical Validation: The provided tables allow traders to check the t-Statistic and R² values to ensure that the observed momentum isn't just noise but a statistically significant trend.

Details

The script operates on a "y ~ x" linear regression model where:

• Independent variable (x): The volatility-adjusted return over the user-defined momentum period.
• Dependent variable (y): The 1-bar lagged log return, also adjusted for volatility.

By calculating the regression over a large lookback (default 1000 bars), the indicator solves for the slope (β₁) and intercept (β₀). Volatility normalization is applied to both variables to ensure the analysis remains consistent across different market regimes and asset scales. The visual output includes a central dashed trendline and surrounding deviation bands that represent the dispersion of residuals around that trend.

Settings

Main Settings

• Regression Lookback: The number of historical bars used to calculate the linear regression model.
• Momentum Period: The lookback period used for calculating volatility-adjusted returns.
• Extend Lines: When enabled, the regression and deviation lines project indefinitely into the future.

Standard Deviation Bands

• Upper Deviation: The multiplier for the upper standard deviation band.
• Lower Deviation: The multiplier for the lower standard deviation band.
• Show Upper Deviation?: Toggles the visibility of the upper band and its associated fill.
• Show Lower Deviation?: Toggles the visibility of the lower band and its associated fill.

Display Options

• Show Table: Toggles the visibility of the statistical summary and signal tables.
• Colors: Customization options for the upper and lower momentum zones.

FAQ

How do I interpret the t-Statistic?

The t-Statistic evaluates the significance of the slope. Generally, an absolute value greater than 1.96 indicates that the momentum slope is statistically significant at a 95% confidence level.

What does the R² value represent?

The R² (Coefficient of Determination) indicates how much of the variance in the returns is explained by the momentum model. Higher values suggest a stronger fit and more reliable momentum.

How can I access Momentum Regression?

You can get access on the LuxAlgo Library for charting platforms like TradingView, MetaTrader (MT4/MT5), and NinjaTrader for free.