A test for stationarity in a time series. The original test (suggested by Dickey and Fuller in 1979) was designed to determine whether an AR(1) model (see autoregressive model) was appropriate:
Here Xj is the value at time j, α is an unknown parameter and εj is a random error. The test statistic is the product of the number of time points and (α̂−1), where α̂ is the ordinary least squares estimate (see method of least squares) of α. The test was extended in 1981 for use with other autoregressive models; the resulting test is called the augmented Dickey–Fuller test or the ADF test. The Phillips–Perron tests are related alternative tests suggested in 1988.
- criterion of identity
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