Cointegration
Quantitative Finance glossary · Market Microstructure & Statistical Arbitrage
Definition
Property that two or more I(1) (unit-root non-stationary) series admit a linear combination that is I(0) stationary: β^T boldsymbolX_t has a stable mean. The basis of pairs trading and statistical arbitrage — the cointegrating residual z_t = Y_t - β X_t is the mean-reverting 'spread' one trades. Tested via Engle-Granger two-step (residual ADF) for bivariate, or Johansen trace/eigenvalue tests for multivariate. Distinct from correlation, which is a same-frequency stationary concept and can be spuriously high for two random walks.
Cointegration in plain English
Two things can each wander around unpredictably on their own, yet stay tethered together — think of a dog owner and their dog on a leash: both roam, but the distance between them keeps snapping back to a comfortable range. Cointegration is the statistical version of that leash: two prices might each drift aimlessly, but a specific combination of them (the 'spread') is stable and keeps returning to its average. Traders love this because if the spread stretches unusually wide, they bet it will snap back — the core idea behind pairs trading. Crucially, it's stronger and more reliable than plain correlation, which can look impressively high between two things that actually have no real link at all (a classic trap called spurious correlation).
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