The Engle-Granger Two-Step Procedure

The Engle-Granger procedure is the classic first test a pairs trader reaches for when checking whether two stocks that individually wander randomly nonetheless move together closely enough to trade a spread between them. Step one is a simple linear regression of one price series on the other, which produces a hedge ratio — the number of shares of the second stock needed per share of the first so that the combined position's price difference, the spread, is the thing left to analyze.

Step two takes that spread — the regression's residual — and runs a standard unit root test (typically the Augmented Dickey-Fuller test) on it. If the spread rejects the unit root, meaning it reliably reverts to a stable level rather than drifting forever, the two series are said to be cointegrated, and the spread is a candidate for a mean-reversion trade: buy the spread when it's unusually low, sell it when unusually high.

A well-known limitation is that the test isn't symmetric — regressing stock A on stock B versus B on A can give slightly different hedge ratios and different test outcomes, since the regression treats one series as the dependent variable — which is one reason the more symmetric Johansen procedure is preferred when testing more than two series at once.