Pair Cointegration & Static Beta Analyzer (v6)

3 時間前

Pair Cointegration & Static Beta Analyzer (v6)

This indicator evaluates whether two instruments exhibit statistical properties consistent with cointegration and tradable mean reversion.
It uses long-term beta estimation, spread standardization, AR(1) dynamics, drift stability, tail distribution analysis, and a multi-factor scoring model.

1. Static Beta and Spread Construction

A long-horizon static beta is estimated using covariance and variance of log-returns.
This beta does not update on every bar and is used throughout the entire model.

Beta = Cov(r1, r2) / Var(r2)
Spread = PriceA - Beta * PriceB


This “frozen” beta provides structural stability and avoids rolling noise in spread construction.

2. Correlation Check

Log-price correlation ensures the instruments move together over time.
Correlation ≥ 0.85 is required before deeper cointegration diagnostics are considered meaningful.

3. Z-Score Normalization and Distribution Behavior

The spread is standardized:

Z = (Spread - MA(Spread)) / Std(Spread)


The following statistical properties are examined:

Z-Mean: Should be close to zero in a stationary process

Z-Variance: Measures amplitude of deviations

Tail Probability: Frequency of |Z| being larger than a threshold (e.g. 2)

These metrics reveal whether the spread behaves like a mean-reverting equilibrium.

4. Mean Drift Stability

A rolling mean of the spread is examined.
If the rolling mean drifts excessively, the spread may not represent a stable long-term equilibrium.

A normalized drift ratio is used:

Mean Drift Ratio = Range( RollingMean(Spread) ) / Std(Spread)


Low drift indicates stable long-run equilibrium behavior.

5. AR(1) Dynamics and Half-Life

An AR(1) model approximates mean reversion:

Spread(t) = Phi * Spread(t-1) + error


Mean reversion requires:

0 < Phi < 1


Half-life of reversion:

Half-life = -ln(2) / ln(Phi)


Valid half-life for 10-minute bars typically falls between 3 and 80 bars.

6. Composite Scoring Model (0–100)

A multi-factor weighted scoring system is applied:

Component Score
Correlation 0–20
Z-Mean 0–15
Z-Variance 0–10
Tail Probability 0–10
Mean Drift 0–15
AR(1) Phi 0–15
Half-Life 0–15

Score interpretation:

70–100: Strong Cointegration Quality
40–70: Moderate
0–40: Weak

A pair is classified as cointegrated when:

Total Score ≥ Threshold (default = 70)

7. Main Cointegration Panel

Displays:

Static beta
Log-price correlation
Z-Mean, Z-Variance, Tail Probability
Drift Ratio
AR(1) Phi and Half-life
Composite score
Overall cointegration assessment

8. Beta Hedge Position Sizing (Average-Price Based)

To provide a more stable hedge ratio, hedge sizing is computed using average prices, not instantaneous prices:

AvgPriceA = SMA(PriceA, N)
AvgPriceB = SMA(PriceB, N)
Required B per 1 A = Beta * (AvgPriceA / AvgPriceB)


Using averaged prices results in a smoother, more reliable hedge ratio, reducing noise from bar-to-bar volatility.

The panel displays:

Required B security for 1 A security (average)

This represents the beta-neutral quantity of B required to hedge one unit of A.

Overview of Classical Stationarity & Cointegration Methods

The principal econometric tools commonly used in assessing stationarity and cointegration include:

Augmented Dickey–Fuller (ADF) Test
Phillips–Perron (PP) Test
KPSS Test
Engle–Granger Cointegration Test
Phillips–Ouliaris Cointegration Test
Johansen Cointegration Test

Since these procedures rely on regression residuals, matrix operations, and distribution-based critical values that are not supported in TradingView Pine Script, a practical multi-criteria scoring approach is employed instead. This framework leverages metrics that are fully computable in Pine and offers an operational proxy for evaluating cointegration-like behavior under platform constraints.

References

[1] Engle & Granger (1987), Co-integration and Error Correction
[2] Poterba & Summers (1988), Mean Reversion in Stock Prices
[3] Vidyamurthy (2004), Pairs Trading
[4] Explanation structured with assistance from OpenAI’s ChatGPT

Regards.

3 時間前

リリースノート

Unnecessary old plot codes were eliminated.