Avaliação do desempenho dos estimadores dos parâmetros no modelo BerG-GARMA

Abstract

This study evaluates the performance of conditional maximum likelihood estimators in the BerG-GARMA model (Bernoulli-Geometric Generalized Autoregressive Moving Average), proposed by Sales, Alencar and Ho (2022), which combines the dynamic structure of GARMA models with the flexibility of the BerG distribution to model count time series with different levels of dispersion. A Monte Carlo simulation study was carried out, considering different sample sizes, three model structures (BerG-GARMA(1,1), BerG￾GARMA(1,0), and BerG-GARMA(0,1)), and three dispersion scenarios (underdispersion, equidispersion, and overdispersion), including cases with negative parameter values. The parameter estimates were obtained using a modified version of the garma package, available on GitHub (https://github.com/matheusbarroso/garma), adapted to incorporate the BerG distribution into the GAMLSS framework, with dynamics applied only to the mean parameter. The performance of the estimators was evaluated using different error metrics. The results indicate that, as the sample size increases, the estimators tend to approach the true values of the model parameters. Additionally, the estimation of the dispersion parameter was found to be more sensitive, especially in contexts with greater variability and smaller sample sizes. The findings extend the results presented by Sales, Alencar and Ho (2022), even when considering variations in the study, such as the inclusion of new scenarios and model structures. It is concluded that the BerG-GARMA model performs well in modeling count time series with varying levels of dispersion and is useful in applications involving data with such characteristics.