Testing the constancy of the thinning parameter in a random coefficient integer autoregressive model

Abstract

Integer-valued autoregressive models are widely used for modeling the time dependent count data. Many of the inference problems related to these types of models are not yet addressed due to the complexities of the related distribution theory. In this paper, we consider one such inference problem associated with these types of models. For a random coefficient integer-valued autoregressive model, we develop a locally most powerful-type test for testing the hypothesis that the thinning parameter is constant across the time. The asymptotic distribution of the suggested test statistic is derived. The Poisson and geometric INAR(1) models are considered for the illustration of the suggested methodology. Simulation studies indicate that the suggested test performs quite well. We have applied our methods to count time series data sets, where the thinning parameter is suspected to be varying.