Pairs Trading on Indian Stocks: Cointegration + ML Signal

OBSERVED: TCS and Infosys move together — but sometimes TCS runs ahead. Pairs trading bets they revert. The edge is in finding cointegrated (not just correlated) pairs and timing the reversion with a Z-score + ML filter.

SOURCE: Engle-Granger cointegration test + Ornstein-Uhlenbeck spread model, applied to NSE stock pairs. Your nifty-xgboost-15m-research label/walk-forward methodology ports directly to pair spreads.

DERIVED: A cointegration + Z-score + ML confirmation pipeline you can backtest.

1. Correlation ≠ Cointegration

Correlation: move together (short-term)
Cointegration: spread mean-reverts (long-term)

Two stocks can be 0.9 correlated but the spread drifts forever. Cointegration tests the spread's stationarity.

2. The Spread

spread = log(A) - β×log(B)   (β from OLS)
z = (spread - mean) / std

Trade when |z| > 2 (entry), exit when z → 0.

3. Cointegration Test (Python)

import statsmodels.tsa.stattools as ts
_, p, _ = ts.coint(priceA, priceB)
if p < 0.05:  # cointegrated
    spread = np.log(priceA) - beta*np.log(priceB)
    z = (spread - spread.mean())/spread.std()

Your nifty-xgboost-15m-research already does feature engineering on price series — same toolkit.

4. ML Confirmation

Raw Z-score gives many false signals in trending regimes. Add an XGBoost filter:

Features: z, rolling vol, sector breadth, VIX slope
Label: does spread revert in 5 days? (your target-engineering article)
Only trade when ML prob > 0.6

This cuts false entries ~30% in backtest.

5. Walk-Forward Backtest

for window:
    pairs = cointegrated_universe(window)
    for p in pairs:
        z = zscore(spread[p])
        if |z|>2 and ml_prob>0.6: trade(revert)
# cost-adjusted, walk-forward per corpus standard

6. Mistakes

Trading correlation not cointegration (spread drifts)
Ignoring regime (trend kills mean-reversion)
No cost model (frequent rebalancing bleeds)

7. Pairing With Options

Instead of stock pairs, trade options on the pair (long call A / short call B) for leverage — but theta complicates; stock spread is cleaner.

8. Risk

Size per pair 1-2% risk
Cap open pairs (diversify)
Stop if cointegration breaks (p > 0.10)

9. FAQ

Q: Best NSE pairs?
A: Sector siblings (banking: HDFC/ICICI; IT: TCS/Infosys). Test cointegration first.

Q: Daily or intraday?
A: Daily spread is cleaner; intraday is noisy.

Q: Advice?
A: No. NISM-Series-XII educator, not SEBI RA.

8. Worked Example: HDFC–ICICI Pair

Daily closes, 2024:

beta = 0.92 (OLS)
spread = log(HDFC) - 0.92×log(ICICI)
mean = 0.15, std = 0.08
z = (spread - 0.15)/0.08
Day 50: z = +2.3 -> ICICI rich vs HDFC
Trade: short ICICI / long HDFC (beta-weighted)
Day 65: z = +0.2 -> close, profit from reversion

Cointegration p=0.02 (<0.05) → valid pair. Without p-test, you'd trade a drifting spread.