I am using Proc Arima to produce the Dickey-Fuller and the augmented Dickey-Fuller tests. According to documentation Proc Arima uses the Dickey-Fuller method that tests the following hypothesis:
H0: psi=0
H1: psi not 0
in the three regressions:
DYt=psi*Yt-1 + ut
DYt=intercept+psi*Yt-1 + ut
DYt=intercept + time trend + psi*Yt-1 + ut
If the series of the residuals (ut) in the above regressions are serially correlated then the regressions should be augmented with lags of the dependent variable (DYt) that is [Sigma (ai*DYt-1)]
The number of lags will be decided upon:
a) the values of information criteria such as AIC and SBIC (run a large number of increasingly augmented regressions starting with 1 augmentation and select the regression with minimum values of the criteria)
or
b) by the rule: Keep augmenting until ut of the regression are not serially correlated.
Based on the above is there an option in Proc Arima that will produce in the output (together with the DF and ADF tests) a statistical test for the serial correlation of the ut (e.g. Darbin Watson) of the equations described above and the values of the Information Criteria (AIC and SIC)? Other econometrics software such as E-Views produces these statistics by default when asking for a unit root test (see http://www.hkbu.edu.hk/~billhung/econ3600/application/app01/app01.html)
Until now i use a manual way to calcualte a) and b) which is very time consuming (e.g. Run the above regressions (and the augmentd cases) with proc reg asking for IC (after creating the DYt, Yt-1 and DYt-1, DYt-2… variables manually with Base SAS), save the residuals with the output statement and run autocorrelation tests (e..g Darbin-Watson).
Best Answer
I do not know Proc Arima. Otherwise your option b seems sounder to me than your option a. I'd recommend against using Durbin-Watson to test for serial correlation in this situation as it is generally considered inappropriate when the dependent variable is included in lagged form as an independent variable.