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# Autocorrelation Pro (Indicator)
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# Autocorrelation Pro Suite (Standard & MTF)
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## 1. Summary
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**Autocorrelation Pro** measures the "Serial Dependence" of market returns. It answers the question: *"Does yesterday's price move predict today's price move?"*
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The **Autocorrelation Pro Suite** is an institutional-grade, high-performance statistical suite comprising two advanced indicators:
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Unlike trend indicators that follow price levels, this proprietary statistical tool analyzes the relationship between the *Current Return* ($R_t$) and the *Previous Return* ($R_{t-1}$). It is a powerful filter for distinguishing between Momentum Regimes and Mean Reversion Regimes.
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* `Autocorrelation_Pro` (Single timeframe separate window oscillator)
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* `Autocorrelation_MTF_Pro` (Multi-Timeframe separate window oscillator)
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## 2. Methodology
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This proprietary suite measures the "Serial Dependence" of market returns in real-time. It directly answers the core quantitative question: *"Does the direction and magnitude of the current price move statistically predict the direction of the next price move?"*
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The indicator calculates the **Lag-1 Pearson Correlation Coefficient** over a rolling window.
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Unlike trend indicators that lag behind price levels (e.g., Moving Averages), the Autocorrelation Suite analyzes the mathematical relationship between the *Current Log-Return* ($R_t$) and the *Previous Log-Return* ($R_{t-1}$). It serves as an ultimate regime filter, allowing quantitative systems to instantly distinguish between persistent Trend Regimes, mean-reverting Oscillation Regimes, and non-directional Random Walks.
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### The Formula
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---
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$$\rho_1 = \frac{\text{Cov}(R_t, R_{t-1})}{\sigma_{R_t} \sigma_{R_{t-1}}}$$
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## 2. Mathematical Methodology
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* **Positive Correlation ($\rho > 0$):** **Momentum Effect.** A positive return is likely followed by another positive return. "Winners keep winning."
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* **Negative Correlation ($\rho < 0$):** **Reversion Effect.** A positive return is likely followed by a negative return (pullback). The market is "choppy" or "elastic".
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* **Zero Correlation ($\rho \approx 0$):** **Random Walk.** The market has no memory; price changes are independent.
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To perform mathematically rigorous correlation sweeps, price series $P_t$ are first transformed into stationary logarithmic returns to prevent spurious statistics:
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*Note: The calculation uses Logarithmic Returns ($\ln(P_t/P_{t-1})$) for statistical accuracy.*
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$$R_t = \ln\left(\frac{P_t}{P_{t-1}}\right)$$
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The calculator computes the **Lag-1 Pearson Correlation Coefficient** ($\rho_1$) over a rolling window of size $N$ (`InpPeriod`):
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$$\rho_1 = \frac{\text{Covariance}(R_t, R_{t-1})}{\sigma_{R_t} \times \sigma_{R_{t-1}}}$$
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### Statistical Interpretations
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* **Positive Correlation ($\rho_1 > \text{Threshold}$):** **Serial Persistence (Momentum).** A positive return is statistically likely to be followed by another positive return. "Winners keep winning." The market is in a sustained Trend Regime.
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* **Negative Correlation ($\rho_1 < -\text{Threshold}$):** **Serial Mean-Reversion (Mean Reverting).** A positive return is statistically likely to be followed by a negative return (immediate pullback). The market is in an oscillating, range-bound, or "choppy" regime.
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* **Zero Correlation ($\rho_1 \approx 0.0$):** **Random Walk (Noise).** Price returns are independent and possess no memory. There is no statistical edge for continuation or reversion.
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---
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## 3. Visualization & Interpretation
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The indicator displays a colored Histogram oscillating between -1.0 and +1.0.
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The indicators display a colored Histogram oscillating between the absolute boundaries of $-1.0$ and $+1.0$.
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* **Green Bars (> 0.1):** **Trend Mode.** The market is exhibiting serial persistence. This is the optimal environment for:
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* Breakout strategies.
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* Moving Average crossovers.
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* Adding to winning positions.
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* **Red Bars (< -0.1):** **Mean Reversion Mode.** The market is oscillating. Prices are rejecting new highs/lows. This is the optimal environment for:
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* Buying Support / Selling Resistance (Range Trading).
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* Fading breakouts (False Breakouts are common).
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* Bollinger Band / RSI strategies.
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* **Gray Bars (-0.1 to 0.1):** **Random Noise.** No clear statistical edge.
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* **Green Bars ($> \text{InpThreshold}$):** **Persistent Trend Regime.** The market exhibits serial continuation.
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* *Optimal Trading Style:* Breakout strategies, Moving Average crossovers, and adding to winning positions (pyramiding).
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* **Red Bars ($< -\text{InpThreshold}$):** **Mean-Reversion Regime.** The market exhibits immediate rejection of new highs and lows.
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* *Optimal Trading Style:* Buying support / selling resistance (Range Trading), fading breakouts, and employing Bollinger Bands or RSI oscillator overbought/oversold systems.
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* **Gray Bars (Neutral Zone):** **Random Noise.** No statistical edge is present. Quantitative systems should stand aside or tighten execution filters.
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## 4. Parameters
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---
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* `InpPeriod`: The lookback window for the correlation calculation (Default: `20`).
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* *Shorter Period (e.g., 10):* Highly reactive, good for scalping.
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* *Longer Period (e.g., 50):* Institutional regime filter.
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* `InpThreshold`: The significance level for coloring (Default: `0.1`).
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* `InpPrice`: The price source to analyze (Default: `PRICE_CLOSE`).
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## 4. Multi-Timeframe Step Alignment (Solving the Live-Bar Warping Bug)
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## 5. Strategic Usage
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Traditional MTF separate-window indicators often suffer from severe visual warping on their right edge. Since the MTF calculation updates tick-by-tick, updating only the latest lower timeframe (LTF) index (`rates_total - 1`) causes the older LTF bars belonging to the current forming HTF block to retain outdated tick values, creating a jagged, diagonal, or fűrészfog-like distortion.
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1. **Trend Filter:** Before entering a trend trade, check the Autocorrelation. If it is **Red (Negative)**, the probability of a sustained trend run is statistically low, even if other indicators say "Buy". Wait for it to turn Green.
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2. **Volatile Breakouts:** If volatility is high but Autocorrelation is **Red**, expect a "V-Top" or "V-Bottom" reversal rather than a clean trend.
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3. **Regime Change:** The transition from Red to Green often marks the moment a consolidation turns into a breakout.
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### The Forming LTF Block Flat-Force Algorithm
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`Autocorrelation_MTF_Pro` resolves this issue by implementing a robust step-blocking design pattern. On every live tick, the indicator dynamically traces back to the very first LTF bar matching the active forming HTF bar:
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```mql5
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int first_bar_of_forming_htf = rates_total - 1;
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while(first_bar_of_forming_htf > 0 &&
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iBarShift(_Symbol, InpTimeframe, time[first_bar_of_forming_htf], false) == 0)
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{
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first_bar_of_forming_htf--;
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}
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first_bar_of_forming_htf++; // Start index of the forming HTF step block
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```
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By forcing the calculation's `start` index back to the beginning of the active block on every tick, the indicator completely overwrites the entire active block uniformly. This guarantees a mathematically correct, perfectly flat horizontal block (Flat Step) on the right edge of the chart in real-time.
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---
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## 5. Input Parameters
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### A. Common Parameters
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* **Period (`InpPeriod`):** The lookback window size for the Pearson correlation calculation (Default: `20`).
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* *Short Window (5 - 15):* Highly reactive, ideal for scalp-level momentum transitions.
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* *Long Window (20 - 50):* Stabilized institutional regime filter.
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* **Significance Threshold (`InpThreshold`):** The correlation level required to trigger color transitions (Default: `0.1`).
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* **Applied Price (`InpPrice`):** The price series source used to compute log-returns (Default: `PRICE_CLOSE`).
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### B. MTF Specific Parameters
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* **Target Timeframe (`InpTimeframe`):** The higher timeframe to calculate autocorrelation on, which is then mapped down to the current chart (Default: `PERIOD_M5`).
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---
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## 6. Strategic Quantitative Usage
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### A. Top-Down Macro Regime Filter (MTF Strategy)
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Before deploying capital on a lower timeframe trend strategy, execute a macro persistence check:
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1. Apply `Autocorrelation_MTF_Pro` on an `M1` execution chart, set to monitor the **`PERIOD_H1`** target timeframe.
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2. If the H1 MTF histogram is strongly **Green**, macro serial persistence is active. You are cleared to trade lower timeframe breakout and momentum trend-following strategies.
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3. If the H1 MTF histogram turns **Red**, macro serial mean-reversion is dominant. Immediately halt trend-following bots and activate range-bound, support/resistance fading systems.
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### B. Regime-Change Breakout Confirmation
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Consolidation phases are characterized by low volatility and near-zero or negative autocorrelation (Red/Gray). The transition of the autocorrelation histogram from **Red/Gray directly into Green** is a leading statistical indicator that a consolidation is turning into a high-velocity, persistent breakout.
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