I have a time series count data by customers that I would like to regress on past months items (count) sold and promotional effects (current and past). Below is an example, and the dataset has one record per customer.
Y= number of items (count) sold
Customer 1: Y/Count data (current month) = Y/count data(past month) + promo data (current month) + promo data (past month)
Customer 2: Y/Count data (current month) = Y/count data(past month) + promo data (current month) + promo data (past month)
I'm not sure what is the right model to use. I could use Dynamic regression/ARIMAX if my response was a continous variable. But the response variable in my hand is a count data, so I'm not sure if ARIMAX is the right model for this problem. In addition, I have lot of zeros in my response variable (similar to zero inflated poisson regression).
I did search in standard textbooks and the internet, I did not come across any regrssion model with time series count data. I would really appreciate if anyone could recommend an appropriate model for this problem.