Asymptotic negative binomial quasi-likelihood inference for periodic integer-valued time series models

This paper establishes the strong consistency and asymptotic normality of the negative binomial quasi-maximum likelihood estimator (NBQMLE) for a general class of integer-valued time series models whose parameters are periodic time-varying. This class of models is specified via its conditional mean,...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2024-01, Vol.ahead-of-print (ahead-of-print), p.1-20
Main Author: Almohaimeed, Bader S.
Format: Article
Language:English
Subjects:
Asymptotic properties
Integers
Maximum likelihood estimators
negative binomial QMLE
Normality
periodic INAR model
periodic INGARCH model
Periodic integer-valued time series models
Time series
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Summary:This paper establishes the strong consistency and asymptotic normality of the negative binomial quasi-maximum likelihood estimator (NBQMLE) for a general class of integer-valued time series models whose parameters are periodic time-varying. This class of models is specified via its conditional mean, which is expressed as a periodic parametric function of (infinite) past observations. An illustration on specific models, namely the Poisson periodic INGARCH model, the negative binomial periodic INGARCH model, and the periodic INAR(1) model is given. In addition, the performance of the NBQMLE is assessed through a simulation study, and an application of the proposed methodology to a real dataset is provided.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2022.2087881