An Overview of ARMA-Like Models for Count and Binary Data

Mirko Armillotta; Alessandra Luati; Monia Lupparelli

doi:10.1007/978-3-031-31186-4_8

An Overview of ARMA-Like Models for Count and Binary Data

Mirko Armillotta, Alessandra Luati, Monia Lupparelli

Research output: Chapter in Book / Report / Conference proceeding › Chapter › Academic › peer-review

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Abstract

A comprehensive overview of the literature on models for discrete valued time series is provided, with a special focus on count and binary data. ARMA-like models such as the BARMA, GARMA, M-GARMA, GLARMA and log-linear Poisson are illustrated in detail and critically compared. Methods for deriving the stochastic properties of specific models are delineated and likelihood-based inference is discussed. The review is concluded with two empirical applications. The first regards the analysis of the daily number of deaths from COVID-19 in Italy, under the assumption both of a Poisson and a negative binomial distribution for the data generating process. The second illustration analyses the binary series of signs of log-returns for the weekly closing prices of Johnson & Johnson with BARMA and Bernoulli GARMA and GLARMA models.

Original language	English
Title of host publication	Trends and Challenges in Categorical Data Analysis
Subtitle of host publication	Statistical Modelling and Interpretation
Editors	Maria Kateri, Irini Moustaki
Publisher	Springer
Chapter	8
Pages	233–274
Number of pages	42
ISBN (Electronic)	9783031311864
ISBN (Print)	9783031311857, 9783031311888
DOIs	https://doi.org/10.1007/978-3-031-31186-4_8
Publication status	Published - 2023

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Name	Statistics for Social and Behavioral Sciences (SSBS)

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10.1007/978-3-031-31186-4_8

An Overview of ARMA-Like Models for Count and Binary DataFinal published version, 1.29 MBLicence: Article 25fa Dutch Copyright Act

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abstract = "A comprehensive overview of the literature on models for discrete valued time series is provided, with a special focus on count and binary data. ARMA-like models such as the BARMA, GARMA, M-GARMA, GLARMA and log-linear Poisson are illustrated in detail and critically compared. Methods for deriving the stochastic properties of specific models are delineated and likelihood-based inference is discussed. The review is concluded with two empirical applications. The first regards the analysis of the daily number of deaths from COVID-19 in Italy, under the assumption both of a Poisson and a negative binomial distribution for the data generating process. The second illustration analyses the binary series of signs of log-returns for the weekly closing prices of Johnson & Johnson with BARMA and Bernoulli GARMA and GLARMA models.",

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An Overview of ARMA-Like Models for Count and Binary Data. / Armillotta, Mirko; Luati, Alessandra; Lupparelli, Monia.
Trends and Challenges in Categorical Data Analysis: Statistical Modelling and Interpretation. ed. / Maria Kateri; Irini Moustaki. Springer, 2023. p. 233–274 (Statistics for Social and Behavioral Sciences (SSBS)).

Research output: Chapter in Book / Report / Conference proceeding › Chapter › Academic › peer-review

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An Overview of ARMA-Like Models for Count and Binary Data

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