Abordagem clássica e bayesiana em modelos autoregressivos para valores inteiros : estudo de caso em número de dias com precipitação em Garanhuns

Abstract

Many aspects of the weather cycle could be described by time series data. Meteorologists often use time series data to assess climate conditions and forecasts. Such models are generally continuous models. The interest was to analyze discrete weather data with the INAR (1) model, using classical and Bayesian approach to parameter estimation. The proposal is to analyze the data series using mixed models with Bayesian approach. Thus, this work is described a sequence of procedures for estimating parameters of autoregressive models of order p = 1, for integer values INAR(1), by classical inference via maximum likelihood estimator and Bayesian inference via simulation Monte Carlo Markov Chain (MCMC). Two alternatives are considered for the a priori density of the model parameters. For the former case is adopted a density non-priori information. For the second, we adopt a density combined beta-gamma. A posteriori analysis is performed by algorithms of MCMC simulation. Also evaluates the prediction of new values of the series number of days with precipitation. The period of analysis comprised 30=11= 1993 to 29=02=2012 and obtained estimates of the period of 31=03=2012 to 28=02=2013. One INAR (1) model of classical parameter estimation and four models INAR (1) Bayesian estimation for the parameters were used. The choice of the most appropriate model the Akaike information criterion (AIC) was used. The analysis of forecast errors was an instrument used to determine which model is best suited to the data. We conclude that the use of MCMC simulation makes the process more exible Bayesian inference and can be extended to larger problems. Mixed models showed better performance than the classical model, mixed among the more robust results than had been the model INAR (1) Poisson-Normal using a priori Beta. Soon we propose the use of thinning operation in mixed models.