Goodness-of-fit tests for Poisson count time series based on the Stein-Chen identity

摘要

To test the null hypothesis of a Poisson marginal distribution, test statistics based on the Stein-Chen identity are proposed. For a wide class of Poisson count time series, the asymptotic distribution of different types of Stein-Chen statistics is derived, also if multiple statistics are jointly applied. The performance of the tests is analyzed with simulations, as well as the question which Stein-Chen functions should be used for which alternative. Illustrative data examples are presented, and possible extensions of the novel Stein-Chen approach are discussed as well.