A comprehensive overview of the literature on models for discrete valued time series is provided, with a special focus on count and binary data. ARMAlike 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.

An overview of ARMA-like models for count and binary data / Mirko Armillotta, Alessandra Luati, Monia Lupparelli. - STAMPA. - (2023), pp. 233-274.

### An overview of ARMA-like models for count and binary data

#### 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. ARMAlike 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.
##### Scheda breve Scheda completa Scheda completa (DC)
2023
Trends and Challenges for Categorical Data Analysis: Statistical Modelling and Interpretation
233
274
Mirko Armillotta, Alessandra Luati, Monia Lupparelli
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Utilizza questo identificatore per citare o creare un link a questa risorsa: `https://hdl.handle.net/2158/1256799`
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