Analysis of Count Time Series: A Bayesian GARMA(p, q) Approach

Extensions of the Autoregressive Moving Average, ARMA(p, q), class for modeling non-Gaussian time series have been proposed in the literature in recent years, being applied in phenomena such as counts and rates. One of them is the Generalized Autoregressive Moving Average, GARMA(p, q), that is suppo...

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Bibliographic Details
Published inÖsterreichische Zeitschrift für Statistik Vol. 52; no. 5; pp. 131 - 151
Main Authors Pala, Luiz Otávio de Oliveira, Carvalho, Marcela de M., Sáfadi, Thelma
Format Journal Article
LanguageEnglish
Published Austrian Statistical Society 11.09.2023
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Summary:Extensions of the Autoregressive Moving Average, ARMA(p, q), class for modeling non-Gaussian time series have been proposed in the literature in recent years, being applied in phenomena such as counts and rates. One of them is the Generalized Autoregressive Moving Average, GARMA(p, q), that is supported by the Generalized Linear Models theory and has been studied under the Bayesian perspective. This paper aimed to study models for time series of counts using the Poisson, Negative binomial and Poisson inverse Gaussian distributions, and adopting the Bayesian framework. To do so, we carried out a simulation study and, in addition, we showed a practical application and evaluation of these models by using a set of real data, corresponding to the number of vehicle thefts in Brazil.
ISSN:1026-597X
DOI:10.17713/ajs.v52i5.1568