ROBUST FITTING OF INARCH MODELS

We discuss robust M-estimation of INARCH models for count time series. These models assume the observation at each point in time to follow a Poisson distribution conditionally on the past, with the conditional mean being a linear function of previous observations. This simple linear structure allows us to transfer M-estimators for autoregressive models to this situation, with some simplifications being possible because the conditional variance given the past equals the conditional mean. We investigate the performance of the resulting generalized M-estimators using simulations. The usefulness of the proposed methods is illustrated by real data examples.