Testing Cointegration for Mean Reversion Pairs Trading
Summary
The document explains how cointegration can identify a mean reverting relationship between non-stationary asset price series. A linear combination of two series that share a stochastic trend may be stationary; deviations of that combination from its mean can then motivate a pairs trade. The article introduces unit root tests used to evaluate stationarity, including Augmented Dickey-Fuller, Phillips-Perron, and Phillips-Ouliaris tests, and distinguishes their assumptions and targets.
Simulated series provide an illustration: two series constructed from a common random walk yield a stationary combination when weighted appropriately, while an arbitrary combination retains evidence of a unit root. This is statistical demonstration, not evidence of live profitability. The article warns that tests can disagree in finite samples and may confuse highly persistent stationary data with non-stationarity. Structural changes can also break an asset relationship, so test results should not be applied mechanically. Strategy construction and trading implementation are deferred to later work.
Key ideas
- Cointegration exists when a linear combination of non-stationary series is stationary.
- A stationary spread can provide a basis for a mean reversion pairs trade.
- ADF, Phillips-Perron, and Phillips-Ouliaris tests assess unit roots or cointegration under different assumptions.
- Simulated common-trend series demonstrate how the correct weights can produce a stationary combination.
- Finite sample uncertainty, persistence, and regime shifts limit the reliability of unit root tests.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.