Semi-parametric goodness-of-fit testing for INAR models
Publication date
2025-07-11
Document type
Forschungsartikel
Author
Organisational unit
Publisher
Bernoulli Society for Mathematical Statistics and Probability
Project Euclid
Series or journal
Bernoulli
ISSN
Periodical volume
31
Periodical issue
4
First page
3213
Last page
3234
Peer-reviewed
✅
Part of the university bibliography
✅
Language
English
Keyword
Bootstrap
Count time series
Goodness-of-fit
Local power
Probability generating function
Semi-parametric estimation
Abstract
Among the various models designed for dependent count data, integer-valued autoregressive (INAR) processes enjoy great popularity. Typically, statistical inference for INAR models uses asymptotic theory that relies on rather stringent (parametric) assumptions on the innovations such as Poisson or negative binomial distributions. In this paper, we present a novel semi-parametric goodness-of-fit test tailored for the INAR model class. Relying on the INAR-specific shape of the joint probability generating function, our approach allows for model validation of INAR models without specifying the (family of the) innovation distribution. We derive the limiting null distribution of our proposed test statistic, prove consistency under fixed alternatives and discuss its asymptotic behavior under local alternatives. By manifold Monte Carlo simulations, we illustrate the overall good performance of our testing procedure in terms of power and size properties. In particular, it turns out that the power can be considerably improved by using higher-order test statistics. In supplementary material, we provide an application to three real-world economic data sets.
Description
First available in Project Euclid: 11 July 2025 (Published: November 2025)
Version
Published version
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Metadata only access