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AdvancedQuantitative MethodsPython

Run this module

cd "Quantitative Methods - Cointegration"
python "cointegration.py"

View source on GitHub

Cointegration & Pairs Trading Foundations

Cointegration: two non-stationary series whose linear combination is stationary. Backbone of statistical arbitrage and pairs trading.

Functions

Function Description
ols_hedge_ratio(y, x) OLS regression for hedge ratio + residuals
adf_test(series, lags) Augmented Dickey-Fuller unit-root test
engle_granger(y, x, lags) Two-step cointegration test
half_life(spread) Mean-reversion half-life via OU fit
zscore_spread(spread, window) Rolling z-score for entry/exit signals

ADF Critical Values (one-sided)

Significance Critical t-stat
1% -3.43
5% -2.86
10% -2.57

t-stat more negative than the threshold → reject unit root → stationary.

Example

from cointegration import engle_granger, half_life, zscore_spread

eg = engle_granger(prices_a, prices_b, lags=1)
if eg['cointegrated_5pct']:
    spread = eg['spread']
    z = zscore_spread(spread, window=60)
    hl = half_life(spread)
    # Enter when |z| > 2, exit when |z| < 0.5

Practical Notes

  • Half-life > 30 days → spread too slow, transaction costs eat profits.
  • Half-life < 1 day → likely noise, not true mean reversion.
  • Cointegration relationships break — re-test rolling windows.
  • For >2 assets use Johansen's test (not implemented here).

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