Goodness‐of‐fit tests for Poisson count time series based on the Stein–Chen identity
Boris Aleksandrov, Christian Weiß, Carsten Jentsch
Abstract
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.
Topics & Concepts
ChenMathematicsPoisson distributionSeries (stratigraphy)StatisticsCount dataGoodness of fitNull hypothesisIdentity (music)Poisson regressionApplied mathematicsDemographyPopulationBiologySociologyAcousticsPhysicsPaleontologyRandom Matrices and ApplicationsBayesian Methods and Mixture ModelsStochastic processes and statistical mechanics