Goodness‐of‐fit tests for Poisson count time series based on the Stein–Chen identity. (9th July 2021)

• Record Type: Journal Article
• Authors: Aleksandrov, Boris; Weiß, Christian H.; Jentsch, Carsten
• Is Part Of: Statistica Neerlandica. Volume 76:Number 1(2022)
• Page Start: 35
• Page End: 64
• Publication Date: 2021-07-09
• Subjects: bivariate Poisson distribution -- bootstrap -- count time series -- diagnostic tests -- INARMA models -- Stein–Chen identity; Statistics -- Periodicals; 519.5; 314.92
• DOI: 10.1111/stan.12252
• Languages: English
• ISSNs: 0039-0402

Abstract

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.