Forecasting the proportion of stored energy using the unit Burr XII quantile autoregressive moving average model

This paper defines the unit Burr XII autoregressive moving average (UBXII-ARMA) model for continuous random variables in the unit interval, where any quantile can be modeled by a dynamic structure including autoregressive and moving average terms, time-varying regressors, and a link function. Our main motivation is to analyze the time series of the proportion of stored hydroelectric energy in Southeast Brazil and even identify a crisis period with lower water levels. We consider the conditional maximum likelihood method for parameter estimation, obtain closed-form expressions for the conditional score function, and conduct simulation studies to evaluate the accuracy of the estimators and estimated coverage rates of the parameters' asymptotic confidence intervals. We discuss the goodness-of-fit assessment and forecasting for the new model. Our forecasts of the proportion of the stored energy outperformed those obtained from the Kumaraswamy autoregressive moving average and beta autoregressive moving average models. Furthermore, only the UBXII-ARMA detected a significant effect of lower water levels before 2002 and after 2013.