Compound Poisson INAR(1) processes: stochastic properties and testing for overdispersion - Schweer, Sebastian; Weiß, Christian (Computational statistics & data analysis, 2014)
The compound Poisson INAR(1) model for time series of overdispersed counts is considered. For such CPINAR(1) processes, explicit results are derived for joint moments, for the k-step-ahead distribution as well as for the stationary distribution. It is shown that a CPINAR(1) process is strongly mixing with exponentially decreasing weights. This result is utilized to design a test for overdispersion in INAR(1) processes and to derive its asymptotic power function. An application of our results to a real-data example and a study of the finite-sample performance of the test are presented.