How to test the variability of count data over time

I'm wondering how I might best test for over-dispersion of raw count data over time. I have just started a project and am exploring my data, so I do not have a model to test on.

I have 4000 independent customers and the frequency of their purchases per day for 44 days. I must determine whether or not customers generally tend to make their purchases in 'clusters' over time; that is, if they tend to engage in 'shopping sprees' and that purchases over time generally tend clump together. The null hypothesis, then, might be "customers are no more likely to repurchase after an initial purchase than they would otherwise".

I realize, then, that I'm working with count data and need to test on their dispersion (I supposed a variance indistinguishable from 0 would indicate that my customers don't engage in shopping sprees and thus I'd fail to reject my null), but I'm not sure how to conduct this examination, since it's not not random count data.

I currently have access to SPSS and would like to perform an analysis with it. Thank you, sincerely, for you help!