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| The ARIMA Procedure |
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, refer to , "PROBDF Function for Dickey-Fuller Tests" in Chapter 4.
Refer to Chapter 4, "SAS Macros and Functions," for a description of the augmented Dickey-Fuller tests. Refer to 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.
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