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Augmented Dickey-Fuller test

The standard test for whether a series has a unit root. The null is that it does; rejecting the null is evidence the series mean-reverts.

The ADF regression fits the change in the series on its previous level plus several of its own lagged changes, and tests whether the coefficient on the previous level is significantly negative. More negative is stronger evidence of reversion.

Reading it: a test statistic of -3.6 against a 5% critical value near -2.9 rejects the unit root, so the series looks mean-reverting on this sample. A statistic of -1.4 does not. Critical values are not the usual normal ones, which is why you read the reported table rather than a standard t-distribution.

Honest caveats: the test has low statistical-power on short samples, so failing to reject proves nothing; it assumes the reversion level is constant, which structural breaks violate; and running it on a hundred pairs to find the twenty that pass is textbook multiple-testing. Validate any pair that passes on out-of-sample data before trading it.

Related: unit-root, stationarity, cointegration, multiple-testing

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