Beta Autoregressive Moving Average Model with the Aranda-Ordaz Link Function

Abstract

In this work, we introduce an extension of the so-called beta autoregressive moving average (βARMA) models. βARMA models consider a linear dynamic structure for the conditional mean of a beta distributed variable. The conditional mean is connected to the linear predictor via a suitable link function. We propose modeling the relationship between the conditional mean and the linear predictor by means of the asymmetric Aranda-Ordaz parametric link function. The link function contains a parameter estimated along with the other parameters via partial maximum likelihood. We derive the partial score vector and Fisher’s information matrix and consider hypothesis testing, diagnostic analysis, and forecasting for the proposed model. The finite sample performance of the partial maximum likelihood estimation is studied through a Monte Carlo simulation study. An application to the proportion of stocked hydroelectric energy in the south of Brazil is presented.

Keywords

• <i>β</i>ARMA models
• double bounded data
• forecasting
• non-Gaussian time series
• parametric link function