topic Re: adf test in proc arima vs proc autoreg in SAS Forecasting and Econometrics

STATIONARITY=

performs stationarity tests. Stationarity tests can be used to determine whether differencing terms should be included in the model specification. In each stationarity test, the autoregressive orders can be specified by a range, test= ar_max , or as a list of values, test=(ar1,...arn) , where test is ADF, PP, or RW. The default is (0,1,2).

PROC AUTOREG, on the other hand, assumes that the specified syntax for the STATIONARITY= option results in models for the ADF test, where the disturbances are distributed as white noise. Therefore, a specification of STATIONARITY=(ADF) assumes that the residuals from the standard Dickey-Fuller test (without any augmenting lags) are white noise. This assumption is noted in the following excerpt from the PROC AUTOREG documentation, however, the default behavior could be more clearly described:

STATIONARITY=(ADF) STATIONARITY=(ADF=(value …value)

produces the augmented Dickey-Fuller unit root test (Dickey and Fuller 1979). As in the Phillips-Perron test, three regression models can be specified for the null hypothesis for the augmented Dickey-Fuller test (zero mean, single mean, and trend). These models assume that the disturbances are distributed as white noise. The augmented Dickey-Fuller test can account for the serial correlation between the disturbances in some way.

For more details on the stationarity tests fit in PROC AUTOREG, please see the following link:

https://go.documentation.sas.com/?docsetId=etsug&docsetTarget=etsug_autoreg_details27.htm&docsetVersion=15.2&locale=en#etsug.autoreg.stationarytsts

I hope this helps explain the difference in the results you obtained when running the two procedures. I will request that the documentation for PROC AUTOREG be updated to further clarify the default behavior for this option. Thank you for your feedback!