A goodness-of-fit test for integer-valued autoregressive processes - Schweer, Sebastian (Journal of time series analysis, 2016)
For autoregressive count data time series, a goodness-of-fit test based on the empirical joint probability generating function is considered. The underlying process is contained in a general class of Markovian models satisfying a drift condition. Asymptotic theory for the test statistic is provided, including a functional central limit theorem for the non-parametric estimation of the stationary distribution and a parametric bootstrap method. Connections between the new approach and existing tests for count data time series based on moment estimators appear in limiting scenarios. Finally, the test is applied to a real data set.