Goodness-of-fit testing of a count time series’ marginal distribution

Christian H. Weiß ()
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Christian H. Weiß: Helmut Schmidt University

Metrika: International Journal for Theoretical and Applied Statistics, 2018, vol. 81, issue 6, No 4, 619-651

Abstract: Abstract Popular goodness-of-fit tests like the famous Pearson test compare the estimated probability mass function with the corresponding hypothetical one. If the resulting divergence value is too large, then the null hypothesis is rejected. If applied to i. i. d. data, the required critical values can be computed according to well-known asymptotic approximations, e. g., according to an appropriate $$\chi ^2$$ χ 2 -distribution in case of the Pearson statistic. In this article, an approach is presented of how to derive an asymptotic approximation if being concerned with time series of autocorrelated counts. Solutions are presented for the case of a fully specified null model as well as for the case where parameters have to be estimated. The proposed approaches are exemplified for (among others) different types of CLAR(1) models, INAR(p) models, discrete ARMA models and Hidden-Markov models.

Keywords: Count time series; Goodness-of-fit test; Estimated parameters; Asymptotic approximation; Quadratic-form distribution; 60G10; 62F03; 62F05; 62M10 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00184-018-0674-z

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