Momentum Regression [BackQuant]

Momentum Regression [BackQuant]

The Momentum Regression is an advanced statistical indicator built to empower quants, strategists, and technically inclined traders with a robust visual and quantitative framework for analyzing momentum effects in financial markets. Unlike traditional momentum indicators that rely on raw price movements or moving averages, this tool leverages a volatility-adjusted linear regression model (y ~ x) to uncover and validate momentum behavior over a user-defined lookback window.

Purpose & Design Philosophy
Momentum is a core anomaly in quantitative finance — an effect where assets that have performed well (or poorly) continue to do so over short to medium-term horizons. However, this effect can be noisy, regime-dependent, and sometimes spurious.

The Momentum Regression is designed as a pre-strategy analytical tool to help you filter and verify whether statistically meaningful and tradable momentum exists in a given asset. Its architecture includes:

Volatility normalization to account for differences in scale and distribution.

Regression analysis to model the relationship between past and present standardized returns.

Deviation bands to highlight overbought/oversold zones around the predicted trendline.

Statistical summary tables to assess the reliability of the detected momentum.

Core Concepts and Calculations
The model uses the following:

Independent variable (x): The volatility-adjusted return over the chosen momentum period.

Dependent variable (y): The 1-bar lagged log return, also adjusted for volatility.

A simple linear regression is performed over a large lookback window (default: 1000 bars), which reveals the slope and intercept of the momentum line. These values are then used to construct:

A predicted momentum trendline across time.

Upper and lower deviation bands, representing ±n standard deviations of the regression residuals (errors).

These visual elements help traders judge how far current returns deviate from the modeled momentum trend, similar to Bollinger Bands but derived from a regression model rather than a moving average.

Key Metrics Provided
On each update, the indicator dynamically displays:

Momentum Slope (β₁): Indicates trend direction and strength. A higher absolute value implies a stronger effect.

Intercept (β₀): The predicted return when x = 0.

Pearson’s R: Correlation coefficient between x and y.

R² (Coefficient of Determination): Indicates how well the regression line explains the variance in y.

Standard Error of Residuals: Measures dispersion around the trendline.

t-Statistic of β₁: Used to evaluate statistical significance of the momentum slope.

These statistics are presented in a top-right summary table for immediate interpretation. A bottom-right signal table also summarizes key takeaways with visual indicators.

Features and Inputs
✅ Volatility-Adjusted Momentum: Reduces distortions from noisy price spikes.
✅ Custom Lookback Control: Set the number of bars to analyze regression.
✅ Extendable Trendlines: For continuous visualization into the future.
✅ Deviation Bands: Optional ±σ multipliers to detect abnormal price action.
✅ Contextual Tables: Help determine strength, direction, and significance of momentum.
✅ Separate Pane Design: Cleanly isolates statistical momentum from price chart.

How It Helps Traders
📉 Quantitative Strategy Validation:
Use the regression results to confirm whether a momentum-based strategy is worth pursuing on a specific asset or timeframe.

🔍 Regime Detection:
Track when momentum breaks down or reverses. Slope changes, drops in R², or weak t-stats can signal regime shifts.

📊 Trade Filtering:
Avoid false positives by entering trades only when momentum is both statistically significant and directionally favorable.

📈 Backtest Preparation:
Before running costly simulations, use this tool to pre-screen assets for exploitable return structures.

When to Use It
Before building or deploying a momentum strategy: Test if momentum exists and is statistically reliable.
During market transitions: Detect early signs of fading strength or reversal.
As part of an edge-stacking framework: Combine with other filters such as volatility compression, volume surges, or macro filters.

Conclusion
The Momentum Regression indicator offers a powerful fusion of statistical analysis and visual interpretation. By combining volatility-adjusted returns with real-time linear regression modeling, it helps quantify and qualify one of the most studied and traded anomalies in finance: momentum.