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What is the best way to convince myself that these data are correlated? that no univariate discrete distribution would approximate them well? that a time series model is necessary to better estimate the future distribution of counts?

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Correlated with what? Each obs to the one before it? – JoFrhwld Aug 4 '10 at 22:26
I'd hope not - the correlation at lag one is very close to 0. – rpierce Aug 5 '10 at 3:37
Or in Prof Wecker's words: "The result was a = .01, which implies little or no serial dependence in the data." – Hibernating Aug 5 '10 at 4:55
up vote 5 down vote accepted

You could just plot the ACF and check if the first coefficient is inside the critical values. The critical values are ok for non-Gaussian time series (at least asymptotically).

Alternatively, fit a simple count time series model such as the INAR(1) and see if the coefficient is significantly different from zero.

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Will the usual dw test be appropriate? – Hibernating Aug 5 '10 at 0:33
The dw test is designed for checking autocorrelation in the residuals from a regression. There is no regression here, so it is not appropriate. – Rob Hyndman Aug 5 '10 at 0:57
I agree. Books mislead again. – Hibernating Aug 5 '10 at 4:47

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