Modelos para séries temporais com dados discretos

Abstract

Time series for discrete data are frequently encountered in various practical applications. In many cases, the data exhibit changes in the frequency of zeros, such as inflation or deflation, and need to be properly handled. To accommodate such characteristics, this work proposes the GARMA Zero-Modified Discrete model family. The major methodological difference is the incorporation of a dynamic and time-variable zero-modification parameter, allowing the model to transition to different zero-modifications at each instant in time. As a main contribution, the GARMA Zero-Modified Skellam model is presented, which extends the formulation to encompass time series in the set of integers. Under the Bayesian paradigm, inference and parameter estimation are performed using the Stochastic Gradient Monte Carlo Hamiltonian algorithm. Sampler efficiency was evaluated in simulation studies for parameter recovery. The applicability and versatility of the models are illustrated in the analysis of three real datasets with distinct behaviors. The results demonstrate that the proposed models adequately capture the structural and dynamic changes in the series' zero modifications, also showing good predictive capacity.