Over-dispersed age-period-cohort models

We consider inference and forecasting for aggregate data organised in a two-way table with age and cohort as indices, but without measures of exposure. This is modelled using a Poisson likelihood with an age-period-cohort structure for the mean while allowing for over-dispersion. We propose a repetitive structure that keeps the dimension of table fixed while increasing the latent exposure. For this we use a class of infinitely divisible distributions which include a variety of compound Poisson models and Poisson mixture models. This results in asymptotic F inference and t forecast distributions.