# Re: st: serial autocorrelation in residuals, what to do?

 From Steven Samuels <[email protected]> To [email protected] Subject Re: st: serial autocorrelation in residuals, what to do? Date Tue, 26 Aug 2008 18:59:38 -0400

Forgive me if this has been mentioned before. -arpois- (Time series regression for counts allowing autocorrelation; type "findit arpois") is a 10-year old module written by Aurelio Tobias and Michael Campbell. I don't know if it will work with recent versions of Stata. You Perhaps it will help, especially if combined with bootstrapped standard errors.

A google search on "count data regression time series" finds a number of references, including this PDF: cameron.econ.ucdavis.edu/research/ CTE01preprint.pdf

-Steve

One plausible explanation for the serial autocorrelation is omitted variables that have some stability over time. This might suggest trying negative binomial regression. You can again look at the autocorrelations among the residuals. Something else to try is a lagged endogenous variable in the Poisson regression. David Greenberg, Sociology Department, New York u.

----- Original Message -----
From: Antonio Silva <[email protected]>
Date: Tuesday, August 26, 2008 1:43 pm
Subject: st: serial autocorrelation in residuals, what to do?
To: [email protected]

________________________________

From: [email protected]
To: [email protected]
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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