# Thread: Proc Arima - DF and ADF tests - AIC and BIC - Error autocorrelation

1. ## Proc Arima - DF and ADF tests - AIC and BIC - Error autocorrelation

Hello,

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 trhee 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/eco...p01/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).

Thanks in advance,

Andreas

2. ## Re: Proc Arima - DF and ADF tests - AIC and BIC - Error autocorrelation

I didn't really get your question. ADF test is included in the proc arima. AIC is usually considered for determination of the lag for the ADF test.

3. ## Re: Proc Arima - DF and ADF tests - AIC and BIC - Error autocorrelation

Hello,

I first run a proc arima with the dickey fuller test without any augmentation. If the residuals of one of the three regressions (i have selected one of them beforehand according to the series i work on) are autocorrelated then i cannot maky any conclysions from the reuslts of the test and i have to run again the test on an augmented regression. But from the output of proc arima i cannot see whether the resiudals are autopcprrelated. Is there any option in proc arima that can show me the autocorrelation of the residuals of the regression i have chosen to apply the DF test? I haven't found any such option until now so i run manually the Dickey Fuller regression i have chosen (one of the three) using proc reg, i save the residuals and then i test the residuals for autocorrelation. If the redisuals are autocorrelated then i run again a series of augmented regressions using proc reg and compare their AIC or SBIC to select one of them. Then i run proc arima with the Augmented DIckey Fuller test with lag the lag determined by the AIC or the BIC. So the second question is if there is an option in proc arima's ADF to provide the AIC or the BIC of the augmented regression on which the dickey fuller test is based on.

So indeed there is an option in proc arima to apply the ADF test but i also need in the output the autocoorelation of the residuals of the Dickey FUller Regression (one of the three) and the AIC and the BIC of the same regression.

In e-views output in the unit root test there is the Darbin Watson test of the Dickey Fuller regression on which the DF test is produced and its AIC and BIC.

I hope i made a bit clearer my question.

Thanks again,

Andreas

4. ## Re: Proc Arima - DF and ADF tests - AIC and BIC - Error autocorrelation

Originally Posted by zarasandreas
Is there any option in proc arima that can show me the autocorrelation of the residuals of the regression i have chosen to apply the DF test?

So the second question is if there is an option in proc arima's ADF to provide the AIC or the BIC of the augmented regression on which the dickey fuller test is based on.
I haven't used SAS for the last two years. So my answer may not be useful. For the first question, I don't think you will get DW statistics but you may get LJung Box statistics for autocorrelation ( try WHITENOISE option). Also one can write a SAS MACRO for relevant output ( extend dftest macro).

For the second question. My understanding is Diagnostic part of the arima give AIC BIC etc. Not sure is it calculating for the model which the dickey fuller test is based on.

5. ## Re: Proc Arima - DF and ADF tests - AIC and BIC - Error autocorrelation

Hello,

Thnaks for your answer. Proc Arima provides the Ljung Box statistics as you say but it provides it for the series Yt under consideration. What it provides has no relation with the error term in the Dickey Fuller Regression. If anybody knows whether there is an option to extract through proc arima an autocorrelation test for ut of the Dickey Fuller regression please share it with me.

Concerning the BIC and the AIC proc arima provides them but they refer to a fitted arima model. So if you request throgh proc arima to fit an arima model the two statisticsare provided but again i haven't found any option to extract throgh proc arima the twi IC for the Dickey Fuller regression. If anybody knows such an option please share it with me.

Andreas

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