Novel goodness-of-fit tests for binomial count time series
Publication date
2022-10-16
Document type
Forschungsartikel
Author
Organisational unit
Publisher
Taylor & Francis
Series or journal
Statistics
ISSN
Periodical volume
56
Periodical issue
5
First page
957
Last page
990
Peer-reviewed
✅
Part of the university bibliography
✅
Language
English
Keyword
Binomial AR(1) model
Bivariate binomial distribution
Count time series
Diagnostic tests
Factorial moments
Stein’s identity
Abstract
For testing the null hypothesis of a marginal binomial distribution of bounded count data, we derive novel and flexible goodness-of-fit (GoF) tests. We propose two general approaches to construct moment-based test statistics. The first one relies on properties of higher-order factorial moments, while the second one uses a so-called Stein identity being satisfied under the null. For a broad class of stationary time series processes of bounded counts with joint bivariate binomial distributions of lagged time series values, we derive the limiting distributions of the proposed GoF-test statistics. Among others, our setup covers the binomial autoregressive model, but includes also other binomial time series obtained, e. g. by superpositioning independent binary time series. The test performance under the null and under different alternatives is investigated in simulations. Two data examples are used to illustrate the application of the novel GoF-tests in practice.
Description
This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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Published version
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