Rolling Hedge Ratios Can Distort Stationarity Tests in Pairs Trading

Summary

The document raises a methodological concern in pairs trading: a trader forms pair spreads using hedge ratios estimated by rolling linear regressions, then applies the Augmented Dickey–Fuller test to those spreads. In the described experiment across a set of assets, shorter estimation windows produce more spreads that appear stationary, while longer windows produce fewer.

This pattern raises the possibility that frequently adapting the hedge ratio changes the spread enough to make a stationarity test look favorable, even when the underlying asset pair does not have a stable mean-reverting relationship. The document is a question rather than a resolved analysis: it provides no answers, diagnostic tests, or empirical results beyond the observation. Researchers should therefore treat rolling-window length as a model choice that can affect inference, and assess the spread construction and testing procedure carefully before interpreting apparent stationarity as evidence for a viable trading strategy.

Key ideas

• The hedge ratio is estimated with a rolling linear regression before constructing each pair spread.
• The author observes more apparently stationary spreads as the hedge-ratio window gets shorter.
• Adaptive hedge ratios can affect the behavior tested by an Augmented Dickey–Fuller procedure.
• The document poses a methodological question but does not provide a resolution or validation results.

Tags

# Pairs Trading - isn't any spread stationary if your rolling lin-reg window is small enough?


# Pairs Trading - isn't any spread stationary if your rolling lin-reg window is small enough?












I have a set of 7 assets, and I have run an ADF test on all possible pair-spreads to find possible pair strategies. I am creating the spreads using a rolling window in which I run linear regression to find the hedge ratio.

It seems that when the rolling window is large/long, few spreads are stationary. But as I decrease the size of the rolling window, more and more spreads becomes stationary. I feel like I'm somehow "cheating" or making a mistake, but I can't figure out what it is.

What is wrong about what I'm doing? Couldn't I take any pair of assets and make a "stationary" spread if I make the rolling window small enough?

EDIT: To be clear, the rolling window I'm referring to is the window of time in which I determine the hedge ratio.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.