Extended generalized autoregressive moving average models for bivariate and univariate time series

• Ano de defesa: 2025
• Autor(a) principal: Ribeiro, Tatiane Fontana
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Bivariate data; Dados bivariados; Dispersão variável; Exponential family; Família exponencial; Intervalo unitário; Monte Carlo simulation; Séries temporais; Simulação de Monte Carlo; Time series; Unit interval; Varying dispersion
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45133/tde-16042025-155615/

This thesis introduces three novel time series models, each addressing different challenges in statistical modeling. First, we propose the bivariate generalized autoregressive (BGAR) model, which extends the vector autoregressive (VAR) model for bivariate time series analysis. The BGAR model allows each time series in the random vector to follow a distribution from the exponential family, enabling the analysis of various data types, including count, binary, and non-normal continuous data. Second, we introduce the unit Dagum autoregressive moving average (UDARMA) model for analyzing time series restricted to the unit interval. This model is based on a new distribution, the unit Dagum (UD), derived from the Dagum distribution. The UDARMA model incorporates autoregressive and moving average terms, explanatory variables, and a link function for the conditional median of the UD distribution. Third, we present the time-varying dispersion generalized autoregressive moving average (VD-GARMA) model, an extension of the generalized autoregressive moving average (GARMA) framework that introduces a dynamic structure for both the mean and dispersion parameters. Unlike standard GARMA models, which assume constant dispersion, the VD-GARMA model allows the dispersion parameter to evolve over time, providing greater flexibility in capturing heteroscedasticity. This model is particularly useful for applications where the variability of the data changes over time, as demonstrated in its application to Brazilian hydroelectric reservoir inflow data. We estimate the parameters of all three models using the conditional maximum likelihood method and provide closed-form expressions for the conditional score vector, Fisher information matrix, and observed information matrix. Monte Carlo simulations are carried out to assess the finite sample performance of the conditional maximum likelihood estimators. The practical usefulness of the models is demonstrated through empirical applications to real-world datasets, including the analysis of the leptospirosis number of cases and hospitalizations, the proportion of useful volume in a water reservoir, the filtering of a normalized difference vegetation index (NDVI) image, and the modeling of Brazilian hydroelectric reservoir inflow. All proposed models outperformed competing approaches in terms of fit and out-of-sample forecasting in each application.