I am doing an analysis of sales-data over a period of time (i.e. over a few years). Those sales-data are also dependent on some predictive variables (i.e. holiday, weekend, weather,...). The daily count has a range of 0 to 10.000 and some zero-values. The problem I am confronted with the choice of a suitable predictive model, that includes the time-structure and the presence of zero values.
I have tried at first a poisson model. The resulting problem was a large overdispersion. To handle the overdispersion I did a Quasi-Poisson- and Negative-Binomial-Model. But here I have the problem of the time-series structure and the poor-predication of zeros (in general the models have a poor prediction-power). For that reason I considered a zero-inflated Poisson-Model (to handle the zeros). Nevertheless the model choice is very poor (so the predictions).
I hope that someone has a idea of a suitable model choice for my modelling problem (and how to handle the ts-structure). The actual results of the models I did, don´t suffice the data.