When a time series has a unit root, the series is nonstationary and the ordinary least squares (OLS) estimator is not normally distributed. Dickey (1976) and Dickey and Fuller (1979) studied the limiting distribution of the OLS estimator of autoregressive models for time series with a simple unit root. Dickey, Hasza, and Fuller (1984) obtained the limiting distribution for time series with seasonal unit roots. Hamilton (1994) discusses the various types of unit root testing.

For a description of Dickey-Fuller tests, see the section PROBDF Function for Dickey-Fuller Tests in Chapter 5. See Chapter 8, The AUTOREG Procedure, for a description of Phillips-Perron tests.

The random-walk-with-drift test recommends whether or not an integrated times series has a drift term. Hamilton (1994) discusses this test.