In this work, we introduce an extension of the so-called beta autoregressive moving average ($\beta$ARMA) models. $\beta$ARMA 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.

This paper proposes robust estimators for parameters of the beta distribution, useful for modelling continuous data restricted to the interval (0,1) in the presence of outliers. Weighted maximum likelihood estimators (WMLE) with two weighting proposals and a minimum distance estimator (MDE) were considered. The bias correction of these estimators was performed using the parametric bootstrap method adapted for data with outliers. The performances of the proposed estimators were evaluated by means of Monte Carlo simulations and their results compared to the performance of the usual estimators by the moment and maximum likelihood methods. The breakdown point and the sensitivity curve were adopted as specic measures of robustness. The numerical evaluation pointed out that the WMLE and MDE have lower sensitivity to outliers and greater breakdown points. The estimators corrected by the proposed bootstrap method had lower bias compared to their versions uncorrected. Moreover, an application to real data is also presented and discussed.