I am trying to model data on the number of online sales are made within a fixed sale period of 3 days. Data are generated only when the sale is made. I think for this kind of data I will be using a type of time series model for count data with inflated zero samples. But this dataset adds one more layer of complexity of the time limit. I don’t know any time series statistical model that limits the length of time. I may consider the stochastic process as a (Poisson like) draw of the limited number of trials: if it’s hourly then 72, if it’s by minutes then 4320 trials. By then, if it’s by minutes, the data ends up with too many zero observations, which ruins the effectiveness of the model. Do you have any better idea?
The data is structured like this:
2011-10-31 07:01:55 2011-11-03 06:59:59 2011-11-02 19:15:39 45
2011-10-31 07:01:55 2011-11-03 06:59:59 2011-11-02 22:32:06 46
2011-10-31 07:01:55 2011-11-03 06:59:59 2011-11-02 23:39:05 47
2011-10-31 07:01:55 2011-11-03 06:59:59 2011-11-02 23:20:09 48
2011-10-31 07:01:55 2011-11-03 06:59:59 2011-11-03 01:32:09 49
2011-10-31 07:01:55 2011-11-03 06:59:59 2011-11-03 03:33:11 50
2011-10-31 07:01:55 2011-11-03 06:59:59 2011-11-03 02:47:07 51
2011-10-31 07:01:55 2011-11-03 06:59:59 2011-11-03 04:05:05 52
2011-10-31 07:01:55 2011-11-03 06:59:59 2011-11-03 04:01:08 53
2011-10-31 07:01:55 2011-11-03 06:59:59 2011-11-03 06:53:09 55
2011-10-31 07:01:55 2011-11-03 06:59:59 2011-11-03 07:00:54 56
The first and second times (1st and 2nd column) are the start and end times of the deal, which is about 3-day apart as the deal lasts for 3 days, and of course fixed for each deal. The third time (in the 3rd column) is increasing as the deal goes by with the cummulative number of items sold on the last columne as a positive integer in the 4th columne. The data is generated only when the sale is made, so the time between succesive sales is irregular, which could be a key term to search for the appropirate model. After further search for the appropriate model, I found integer autoregressive model (INAR) may be used, but I am not sure... Since the sale is recorded by the second, I may think the data series with T=259200 observations having many (too many!) zero observations. I may transform the data by minutes by summing over the sales numbers withine one minute to reduce to T=4320. This will reduce the ratio of zero-total observations smaller, and apply INAR or some kind of zero-inflated stochastic model (truncated poisson or something like that). Could you give me any good ideas?