On modelling of time series of count data with marginal compound distributions

In this talk, we introduce a class of models for time series of count data that allow a flexible treatment 
of time dependence as well as nonstationarity, while preserving marginal properties.  
The models are based on stochastic processes derived from the convolution of compound Poisson random variables 
with a kernel function. In the stationary setting, kernel functions are defined by probability 
density functions and capture the underlying dependence structure in a computationally efficient manner. 
We further develop regression models for count data where the shape of the kernels 
depends on covariate information to obtain rich dynamics. The parametric specification 
of the kernels we propose strikes a balance between tractability and the ability to capture 
complex dependence structures, and also allows parameter estimation and prediction 
based on bivariate distributions. We illustrate the construction by modeling real 
data in crime analysis and epidemiology.