Modelo Weibull autorregressivo de médias móveis: um novo modelo para aplicações em séries de vazão e velocidade do vento

Abstract

Hydroclimatic processes, such as streamflow and wind speed, have a probabilistic nature since they suffer interference from an infinite number of random factors. Most of the time series within the natural sciences also consist in autocorrelated processes. These characteristics make it interesting to use autoregressive moving average (ARMA) models for analysis and prediction of hydroclimatic data. ARMA models absorb the series self-correlation in its structure. The most traditional class of ARMA models has the normality of the data as a premise. However, it is recognized that the Gaussian assumption is too restrictive for many applications. Streamflow and wind speed data, for example, can be modeled more adequately by the Weibull distribution, which presents asymmetry in its histogram and is inferiorly limited by zero. Thus, the goal of this work is to propose a dynamic model for time series with Weibull distribution, as a tool for analyzing autocorrelated hydroclimatic data. In the proposed model, called Wei-ARMA, the mean is modeled by a dynamic structure containing autoregressive and moving averages components, regressors and a link function. The work also proposes a parametric trend test based on the Wei-ARMA model to analyse the presence of trend in autocorrelated data series. The estimation of parameters was performed considering the conditional maximum likelihood method and a Monte Carlo simulation was employed to evaluate the performance of the estimators and the proposed trend test in different scenarios. The estimators were evaluated in terms of relative bias and mean square error, while the trend test was evaluated in terms of size and power, and compared with usual non-parametric trend tests, such as the Mann-Kendall test and Seasonal Mann-Kendall test. The conditional maximum likelihood estimators performed well and the proposed trend test obtained better results than the concurrent tests. Finally, the applicability of the proposed model and trend test was evaluated in streamflow and wind speed monthly series. The Wei-ARMA model was able to absorb the behavior characteristics of the data, obtaining similar or better results compared to the traditional ARMA model, having as main advantage not predicting negative values.