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Augmented Dickey-Fuller Test

The augmented Dickey-Fuller test (ADF test) is a statistical test for a unit root in a time series. A common regression form is

DeltaX_t=alpha+betat+gammaX_(t-1)+sum_(j=1)^pdelta_jDeltaX_(t-j)+epsilon_t,

where the intercept and time trend may be omitted. The null hypothesis gamma=0 is tested against the alternative hypothesis gamma<0. Applying the difference operator at lags j=1, ..., p allows for serial dependence beyond a first-order autoregression.

The null distribution of the test statistic is not the usual Student's t-distribution, so Dickey-Fuller critical values are used. The choice of lag order affects both the size and power of the test.

See also

Autoregressive Model, Difference Operator, Nonstationary Time Series, Null Distribution, Stationary Time Series, Unit Root

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References

Dickey, D. A. and Fuller, W. A. "Distribution of the Estimators for Autoregressive Time Series with a Unit Root." J. Amer. Statist. Assoc. 74, 427-431, 1979. https://doi.org/10.1080/01621459.1979.10482531.Said, S. E. and Dickey, D. A. "Testing for Unit Roots in Autoregressive-Moving Average Models of Unknown Order." Biometrika 71, 599-607, 1984. https://doi.org/10.1093/biomet/71.3.599.

Cite this as:

Weisstein, Eric W. "Augmented Dickey-Fuller Test." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AugmentedDickey-FullerTest.html

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