st: serial autocorrelation in residuals, what to do?

 From Antonio Silva To Subject st: serial autocorrelation in residuals, what to do? Date Tue, 26 Aug 2008 13:43:04 -0400

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From: asilva100@live.com
To: statalist@hsphsun2.harvard.edu
Subject: serial autocorrelation in residuals, what to do?
Date: Mon, 25 Aug 2008 22:53:46 -0400

Hello Statalist:
Well, again I must resort to you for help. Here is the situation. I ran a Poisson model of the following sort:

y = x1 + x1squared + X2 + X3 + X4

The results were very good. I hypothesized that there was an inverse U-shaped relationship between X1 and the dependent variable, and the results supported this--in other words, X1 was positive, and X1squared was negative, and both coefficients were significant. Also, the inflection point was within the range of the data.
However, I sent the paper out for review, and a reviewer suggested I test for autocorrelation. I asked for help, and members of this great list helped me. I found that there was no autocorrelation of the Poisson counts themselves (they are yearly counts). However, next, based on advice I received from members of this list, I tested for autocorrelation of the residuals (using GLM and the predict dev command) and found out that the residuals were highly correlated. In short, the residuals are not independent.
I am stuck. I have tried everything to resolve this problem. First, I tried transforming X1 and X1squared (the variables of most interest) by using first differences for both. When I did this, it eliminated the autocorrelation among the residuals, but the model blew up and X1 and X1squared became highly insignificant. Second, I tried adding omitted variables. This helped, but not enough.
I am writing to see if anyone has any ideas about what I should do from here. I
figure I have three options.
1. I can give up.
2. I can try a different transformation of the variables of interest (any ideas?). or
3. I can cite some work that says that serial autocorrelation of residuals in Poisson regression is not that big of a problem. (I figure this may be the case because including the squared term in the model virtually assures that the residuals will be correlated).
Any advice is welcome and appreciated. Thanks again for all your help.
Antonio Silva

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