Inflated beta autoregressive moving average models

In this paper, we introduce the inflated beta autoregressive moving average (Iβ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}ARMA) models for modeling and forecasting time series data that assume values in the intervals (0,1], [0,1) or [0,1]. The proposed model considers a set of regressors, an autoregressive moving average structure and a link function to model the conditional mean of inflated beta conditionally distributed variable observed over the time. We develop partial likelihood estimation and derive closed-form expressions for the score vector and the cumulative partial information matrix. Hypotheses testing, confidence interval, some diagnostic tools and forecasting are also proposed. We evaluate the finite sample performances of partial maximum likelihood estimators and confidence interval using Monte Carlo simulations. Two empirical applications related to forecasting hydro-environmental data are presented and discussed.