topic Re: Understanding the Durbin-watson statistic in SAS Forecasting and Econometrics

Understanding the Durbin-watson statistic

Azhar2 — Sun, 07 Nov 2021 00:04:49 GMT

Hi all

Thanks in advance for reviewing my question.

I have panel data over 10 periods for 5000 individual customers. I am doing a proc panel

MODEL change_in_consumption = current_income + change in previous consumption

I ran a DW test and got the result below.

Can someone help me understand the upper and lower.

I understand the statistic 1.87 indicative of negative correlation, right? and 2.13 is vice versa. Are these results significant?

Thanks

Re: Understanding the Durbin-watson statistic

PaigeMiller — Sun, 07 Nov 2021 15:45:53 GMT

I have never used Durbin Watson, so I don't know the answer, but I'm pretty sure Google knows.

Re: Understanding the Durbin-watson statistic

sbxkoenk — Sun, 07 Nov 2021 20:25:09 GMT

Calling @SASCom1 !

I do not understand Durbin-Watson statistic fully in PROC PANEL output neither.

In PROC AUTOREG, you get something like:

, and that's much easier to understand.

[EDIT]
I also think that 1.87 is the test statistic value for White Noise vs. Positive Correlation hypothesis test
and 2.13 is the test statistic value for White Noise vs. Negative Correlation hypothesis test.

This would mean that the 'White Noise vs. Positive Correlation' label should span across the 1.87 statistic value as well.
The 'rectangles' in the table (the division of the table) are not entirely correct to me.

Thanks,
Koen

Re: Understanding the Durbin-watson statistic

SASCom1 — Wed, 10 Nov 2021 18:02:28 GMT

The interpretation of Durbin-Watson test output in PROC PANEL is discussed here:

https://go.documentation.sas.com/doc/en/pgmsascdc/v_018/etsug/etsug_panel_details69.htm#etsug.panel.dw

The output shows test results for three tests as discussed in the above section, (1) white noise vs. positive correlation, (2) random walk vs. stationarity, (3), white noise vs. negative correlation. The first 2 tests reported d_rho, while the third test reported is 1-d_rho. In your output, d_rho = 1.87 which applies to the first two tests, 1-d_rho = 2.13, which applies to the third test.

The reason that two p values (Pr<DWLower and Pr<DWUpper) are produced for these tests is also discussed in the above section:

In finite samples, the mechanics of the Durbin-Watson test produce an indeterminate region, which is a region of uncertainty about whether to reject the null hypothesis. Because of this ambiguity, all three tests report two p-values. The first test and the third test produce Pr < DWLower and Pr < DWUpper.

How to interpret DW test p values is also discussed in the above section :

For the first and the third test, Pr < DWLower is always greater than or equal to Pr < DWUpper. If Pr < DWLower is less than or equal to the significance level, then the null hypothesis that rho = 0 is rejected. If Pr < DWUpper is greater than or equal to the significance level, then the null hypothesis is accepted. These two p-values get closer when N increases.

Because your Pr < DWLower for the positive correlation test is smaller than 0.0001, you reject the null of rho = 0 and conclude with positive autocorrelation. Because your Pr<DWUpper for the negative correlation test is equal to 1, greater than significance level, you accept the null and conclude that there is no negative autocorrelation.

I hope this helps.

Re: Understanding the Durbin-watson statistic

SASCom1 — Thu, 11 Nov 2021 22:35:10 GMT

Sorry, "1-d_rho" below is a typo, it should be 4-d_rho:

The first 2 tests reported d_rho, while the third test reported is ~~1-d_rho~~ 4-d_rho. In your output, d_rho = 1.87 which applies to the first two tests, ~~1-d_rho~~ 4-d_rho = 2.13, which applies to the third test.