Tests for Integer-valued Time Series Based on the Probability Generating Function

This paper addresses models for time series of integer-valued variables. Such series arise in various applications, often as increment series for counts of interest. A model with a GARCH-type structure with the Skellam conditional distribution is considered. We propose a novel testing procedure to assess the null hypothesis that a set of integer-valued observations follows such model. The proposed test statistic incorporates the empirical probability generating function computed from the data.