Modelo Dinâmicos Fréchet-Gama com aplicações a dados Correlacionados de Múltiplos Observadores Meteorológicos

Abstract

State Space Models are versatile and powerful tools for modeling and analyzing time series. Their unified approach allows them to address a wide variety of models, whether univariate or multivariate, granting them a central role in several fields of knowledge. One such field is climatology, where the analysis of meteorological time series becomes essential in the current context of climate change. Understanding the behavior of climatic factors, such as storms and thunderstorms, is crucial for studying atmospheric dynamics and their implications. In this study, we analyze the time series of the monthly maximum hours of thunderstorms recorded by surface meteorological stations located at Ponta Pelada (SBMN) and Eduardo Gomes (SBEG), situated in the southern and western zones of Manaus, respectively, and under the management of the Brazilian Air Force (COMAER). The analyzed series spans the period from January 1982 to December 2024. The modeling, analysis, and forecasting will be conducted using the methodology of Generalized Dynamic Linear Models (GDLMs), associated with the Fréchet distribution, which belongs to the exponential family of observational distributions. The theoretical framework for these models is based on the works of Migon (1984), Migon and Harrison (1985), and West, Harrison, and Migon (1985). For predictive analysis, we adopt the metric described by Petris, Petrone, and Campagnoli (2008), specifically in Chapter 3 of their book. Finally, comparisons will be made between simulated values, observed data, and the predictions generated by the GDLM to assess the efficiency and accuracy of the proposed model. This study highlights the relevance of State Space Models, particularly in climatology, contributing to the understanding and forecasting of extreme climatic events in the Amazonian context.