medium · Quantitative Finance microstructure-arb
An analyst estimates the hedge ratio using OLS but finds that the residuals are heteroskedastic.
How does this affect the Dickey-Fuller test for cointegration?
- It has no effect at all, since the Dickey-Fuller stat only examines the sign of changes.
- It can lead to incorrect p-values and false conclusions about stationarity if not corrected.
- It automatically proves the two series are cointegrated with a stable long-run equilibrium.
- It implies the estimated hedge ratio β is itself biased, inconsistent, and unreliable going forward.
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