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October 16

Testing Poisson Model Assumptions on a Subset of Data

I have data on how many customers visited a store each day during the last quarter, and I've fit a Poisson distribution to it. The number of visits per day is stationary and not autocorrelated throughout the 3 months in the quarter. I want to estimate the number of visits for an arbitrary month: do I need to verify the data is stationary and without autocorrelation over a month-long time frame as well? OldTimeNESter (talk) 15:16, 16 October 2013 (UTC)[reply]

Theoretically yes, in practice probably not. In principle it is possible for there to be statistical structure during part of the interval that reverses direction during the other part of the interval, but that sort of thing hardly ever happens. But the claim that visits are stationary and not autocorrelated is hard to believe. Do you really get the same number of visits on every day of the week? That hardly ever happens in a store. Looie496 (talk) 16:15, 16 October 2013 (UTC)[reply]

I don't understand Looie's passage But the claim that visits are stationary and not autocorrelated is hard to believe. Do you really get the same number of visits on every day of the week? Stationary and not autocorrelated does not mean the number is fixed -- it means the daily numbers are independent draws from a fixed distribution. Duoduoduo (talk) 21:22, 16 October 2013 (UTC)[reply]

Is it likely that the daily visits are independently and identically distributed? This visits to this store must be unusually predictable. I'd guess there would be day-of-the-week effects and month-of-the-year effects. EdJohnston (talk) 00:59, 17 October 2013 (UTC)[reply]

(OP here). I counted the number of visits for each day from May 1 to July 31, not on each Monday, Tuesday, etc. I looked at autocorrelations in SPSS and found none, and then compared the distributions by month with the Kruskal-Wallis test and found no significant difference. So I believe that for the 3 month period, the data is not autocorrelated and is stationary. What I'm wondering is if I can extend this inference to any of the three one-month periods: it seems plausible that the data may be autocorrelated in (say) May, but not from May to July. But I'm not sure if this is a legitimate worry. OldTimeNESter (talk) 15:39, 17 October 2013 (UTC)[reply]