mql5/Indicators/MyIndicators/Quant/VarianceRatio_Pro.md

Variance Ratio Pro (Indicator)

1. Summary

Variance Ratio Pro is a statistical tool designed to test the Random Walk Hypothesis on financial time series. It acts as a high-level regime filter by analyzing the speed of volatility expansion.

Unlike trend indicators (Moving Averages) that lag, or oscillators (RSI) that saturate, the Variance Ratio measures the structural properties of price movement. It answers: "Is the market trending (persistent), reverting (anti-persistent), or random?"

2. Methodology & Logic

The indicator is based on the Lo-MacKinlay Variance Ratio Test. Ideally, if a market is a Random Walk, the variance of returns should scale linearly with time (Variance of 2-day returns should be exactly 2x the variance of 1-day returns). Deviation from this linearity reveals the market state.

The Formula

VR(q) = \frac{\text{Var}(r_q)}{q \times \text{Var}(r_1)}

• Var(r_1): Variance of 1-period log returns over window N.
• Var(r_q): Variance of $q$-period log returns over window N.

Interpretation

The indicator oscillates around 1.0.

• VR > 1.0 (Green): Trend Phase (Persistence). The market is moving in a specific direction faster than randomness would dictate. This is often called "Mean Aversion" (running away from the average).
• VR < 1.0 (Blue): Mean Reversion (Anti-Persistence). The market is pulling back. A step forward is likely followed by a step back. Volatility is contracting relative to time.
• VR ≈ 1.0 (Gray): Random Walk. The market is efficient and unpredictable. Price action is noise.

3. MQL5 Implementation Details

• Engine (VarianceRatio_Calculator.mqh):
  • Optimization: Uses a Sliding Window algorithm for variance calculation. Instead of recalculating the entire summation loop for every bar (which would be slow), it incrementally updates sums as the window slides, ensuring O(1) performance even with large lookback periods.
  • Price Engine: Contains integrated logic to handle both Standard and Heikin Ashi price sources efficiently.
• Visuals:
  • Uses DRAW_COLOR_HISTOGRAM centered at 1.0 for intuitive reading.

4. Parameters

• InpWindow: The sample size (N) for the variance calculation (Default: 64). Larger windows give smoother, more reliable signals but are slower to react.
• InpLag: The aggregation period (q) (Default: 2). A lag of 2 compares 2-bar returns to 1-bar returns, making it very sensitive to short-term autocorrelation.
• InpPrice: The price source (Close, High, Low, etc.). Recommendation: Use PRICE_CLOSE (Raw Price) for statistical validity.

5. Strategic Usage

1. Trend Confirmation: Only enter breakout trades when the histogram is Green (VR > 1.0) and rising. This confirms the breakout has "momentum memory".
2. Fade/Reversal Filter: If looking for a reversal trade, wait for the histogram to turn Blue (VR < 1.0). This confirms the trend structure has broken and the market is now mean-reverting.
3. Noise Filter: Avoid trading when the histogram is Gray (around 1.0). The market is random, and technical signals are likely false positives.