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.
Armillotta, M., Luati, A., Lupparelli, M. (2023). An Overview of ARMA-Like Models for Count and Binary Data. In Trends and Challenges in Categorical Data Analysis (pp. 233-274). Springer [10.1007/978-3-031-31186-4_8].
An Overview of ARMA-Like Models for Count and Binary Data
Mirko Armillotta;
2023-01-01
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.File | Dimensione | Formato | |
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