Aplicação em modelos de variação autorregressiva condicional baseada na distribuição Birnbaum-Saunders

Abstract

The conditional autoregressive variation (CARR) model proposed by Chou (2005) proved to be efficient in estimating asset price volatility. However, the estimation requires an adequate error density, where the Weibull distribution is commonly used. Xie & Wu (2017) proposed a model based on gamma distribution (GCARR), with satisfactory results in inlier and outlier problem reduction. In this work, we propose the conditional autoregressive variation model based on the Birnbaum-Saunders distribution (BSCARR). We implemented an approach based on the maximum likelihood method to obtain the parameter estimates and derive measurements for residue analysis and diagnosis. We then carried out a simulation and Monte Carlo study with the objective of evaluating the performance of the maximum likelihood estimators of the proposed model. Finally, we illustrate the proposed methodology using a set of real data.