Modelos para Séries Temporais de Contagem: implementação dos modelos GLARMA e INGARCH no Software R

Abstract

The time series models developed by Box and Jenkins in 1970 constitute the main class of current temporal models, the so-called ARMA (Autoregressive Moving Average) models. Although these models are popular in many areas, their application to counting series, composed of discrete values that represent specific events such as number of customers or disease cases, presents unique challenges. In this context, models that use counting probability distributions, the main ones being Poisson and Negative Binomial, prove to be important tools for this type of data. Thus, the aim of the work was to describe the implementation of the GLARMA (Generalized Linear Autoregressive Moving Average) and INGARCH (Integer-valued Generalized Autoregressive Conditional Heteroscedasticity) models in the R software package fableCount. In addition to the mathematical and statistical definitions of estimation and forecasting for each model, computational aspects were also developed, including numerical estimation methods, construction of prediction intervals via bootstrap, and time series cross-validation procedures. Another important feature of the package explained in the work are the automated modeling algorithms, divided into: automatic distribution selection, automatic parameter order selection and automatic model selection for forecasting. For the application, epidemiological data were used, where a significant improvement in both forecasting performance and interpretability was observed when using count time series models compared to ARMA and NNETAR models. At the end, package usage metrics and future development plans are described.