Pairs Trading Cointegration Pro (Indicator)

1. Summary (Introduction)

The Pairs Trading Cointegration Pro is an institutional-grade, high-performance separate window statistical arbitrage oscillator. While traditional pairs trading methods in retail trading rely simply on price correlation (which is highly unstable and prone to terminal spread drift), PairsTrading_Pro measures true cointegration using a dynamic rolling Ordinary Least Squares (OLS) mathematical engine.

The indicator dynamically calculates the rolling Hedge Ratio (\beta) and Intercept (\alpha) between any two assets (default: Brent vs. WTI Crude Oil), extracts the volatility-normalized spread, and plots a stacioner Z-Score as a 5-Zone Thermal Color Histogram.

Featuring VWAP-style Anchored Resets (Session, Weekly, Monthly, and Custom Session), the indicator can completely isolate intraday/intraweek price relationships from overnight gaps and illiquidity, making it the ultimate tool for active statistical arbitrage.

2. Mathematical Foundations and Calculation Logic

The mathematical structure dynamically recalculates the cointegrated relationship at each bar i over a rolling or anchored window of size N (window_size):

A. Rolling Ordinary Least Squares (OLS)

The indicator calculates the rolling mean of the Asset A (\bar{A}) and the Benchmark B (\bar{B}). It then solves the OLS regression of A on B to find the dynamic Hedge Ratio (\beta) and Intercept (\alpha):

\beta_i = \frac{\text{Covariance}(A, B)}{\text{Variance}(B)} \alpha_i = \bar{A}_i - (\beta_i \times \bar{B}_i)

B. Dynamic Spread and standard deviation

The spread at each bar t within the window is calculated. Because we subtract the OLS intercept (\alpha_i), the rolling mean of this spread over the window is algebraically guaranteed to be exactly 0.0:

\text{Spread}_{t} = A_{t} - \beta_i B_{t} - \alpha_i \quad \text{for } t = i-N+1 \dots i

The sample standard deviation (\sigma_{\text{spread}}) of the spread over the active window is computed:

\sigma_{\text{spread}} = \sqrt{\frac{1}{N-1} \sum_{k=0}^{N-1} (\text{Spread}_{i-k})^2}

C. Volatility-Normalized Z-Score

The final Z-Score is calculated, representing how many standard deviations the current spread has drifted away from its statistical equilibrium of 0.0:

Z_i = \frac{\text{Spread}_i}{\sigma_{\text{spread}}}

3. MQL5 UI & Architecture

Decoupled Math Engine (PairsTrading_Calculator.mqh): All covariance, variance, rolling OLS, and Z-Score computations are encapsulated inside the highly optimized CPairsTradingCalculator include class.
Strict O(1) Real-Time Tick Optimization: The calculator uses the platform's prev_calculated parameter to process only the newest incoming bar on every tick. This keeps CPU usage at absolute zero, allowing the Z-Score to update live in real-time.
VWAP-Style Anchored Resets: In addition to standard rolling windows (InpLookback), the indicator supports dynamic resets:
- Daily Reset (ANCHOR_SESSION): Resets daily. Excellent for intraday trading.
- Weekly Reset (ANCHOR_WEEK): Resets weekly. Ideal for swing trading.
- Custom Session (ANCHOR_CUSTOM_SESSION): Resets at a user-defined broker-time range (e.g. 09:00 to 18:00). It completely filters out overnight gaps and illiquid trading hours, leaving the Z-Score flat/empty (EMPTY_VALUE) during inactive periods.
Advanced Bar-Time Synchronization: PairsTrading_Pro aligns Symbol A and Symbol B prices perfectly by timestamp using iBarShift(..., false) and iClose, ensuring that different market open/close times or missing bars do not distort the calculation.
Hardlocked Scale Bounds [-3.5, 3.5]: To prevent single extreme black-swan spikes (e.g., Z-score hitting -10.0 during oil gaps) from squishing the entire historical chart into an unreadable flat line, the separate window's scale is fixed between -3.5 and 3.5. Outliers are simply clipped at the boundaries, maintaining a perfect, consistent visual aspect ratio across all timeframes.

4. Parameters

Symbol A (InpSymbolA): The primary asset to trade (Default: "UKOIL" - Brent Crude Oil).
Symbol B (InpSymbolB): The secondary benchmark asset (Default: "USOIL" - WTI Crude Oil).
Anchor Reset (InpAnchor): The reset anchor period (None, Session, Week, Month, Custom Session).
Lookback (InpLookback): The rolling regression window size (Used if Anchor = None).
Custom Start (InpCustomStart): Session start time in format "HH:MM" (Used if Anchor = Custom).
Custom End (InpCustomEnd): Session end time in format "HH:MM" (Used if Anchor = Custom).

5. Advanced Statistical Arbitrage Strategies

A. Classic Spread Execution (Mean Reversion)

Buy the Spread (Z \le -2.0 - DeepSkyBlue): Symbol A is extremely underpriced relative to Symbol B.
- Action: BUY Symbol A (Long) and SELL Symbol B (Short) with equal cash exposure.
Sell the Spread (Z \ge 2.0 - OrangeRed): Symbol A is extremely overpriced relative to Symbol B.
- Action: SELL Symbol A (Short) and BUY Symbol B (Long) with equal cash exposure.
The Exit (Z \to 0.0 - Gray): When the histogram returns to the middle 0.0 axis, the spread has returned to its statistical equilibrium. Close both legs simultaneously to lock in the mean-reversion profit.

B. The Quant-Grade Synergy: Cointegration + LLD Pro (Single-Leg Trading)

A major drawback of classic pairs trading is that opening two legs is capital-intensive and subject to double-broker execution slippage. By combining PairsTrading_Pro with the LLD_Pro (Lead-Lag Dominance) indicator, you can trade a single, high-probability leg:

Identify the Spread Extremes: PairsTrading_Pro alerts you that the spread is extremely cheap (e.g., Z = -2.5, meaning Symbol A is cheap, Symbol B is expensive).
Identify the Leader: Open the LLD_Pro indicator for the two symbols.
- If Symbol B (WTI) is the Leader (leads Symbol A / Brent): WTI has already moved, and Brent (Symbol A) is mathematically guaranteed to follow to close the gap. Since Symbol A is currently too cheap, you simply BUY Symbol A (Brent) as a single directional trade!
- This allows you to trade with half the margin requirement and zero execution hassle, leveraging the leader's predictive momentum to capture the gap-reversal.

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