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In determining if there is any serial correlation in a time series of count data, is the Durbin-Watson statistic or similar approaches appropriate?

I ask this question because the dwtest implemented in R can take an lm object as an input, but my time series comprises count data, which can be approximated by a negative binomial distribution, and lm would not be the appropriate model choice.

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    $\begingroup$ The Durbin-Watson test is never appropriate. Even if you are only interested in first order autocorrelation in the absence of lagged dependent variables, there are better tests. $\endgroup$ – tchakravarty Feb 5 '15 at 9:17
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    $\begingroup$ Thanks for your comment. If you don't mind, could you elaborate on why it's not appropriate and what the better tests are (and why they're better)? $\endgroup$ – mamboSC4649 Feb 7 '15 at 10:20
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    $\begingroup$ As indicated in my comment, the DW has several severe shortcomings other than the fact that it is a bounds test, so is often inconclusive: it only tests for first-order serial correlation; is not appropriate when you include a lagged dependent variable in your regression... Please see any undergraduate text on econometrics for better (more general, more powerful) tests, such as the Breusch-Godfrey LM test. A very nice introduction is in Baltagi's Econometrics, Chapter 5. $\endgroup$ – tchakravarty Feb 7 '15 at 10:25
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DW test is test for first order residual autocorrelation. I do not see any reason why it could not be used for testing the residual serial independence.

Of course there are newer tests for that.

I think it could tell you something about the specification of your model. Even if you model count data it might tell that you need to add lagged values into your glm estimated model.

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