A dynamical regression model for double-bounded time series based on the reflected unit Burr XII distribution

Abstract This paper introduces a new time series model based on the reflected unit Burr XII (RUBXII) distribution that is an alternative to the Kumaraswamy autoregressive moving average and Beta autoregressive moving average models for time series analysis taking values in the standard unit interval. The proposed model describes the conditional median of RUBXII-distributed discrete-time series by a dynamic structure that includes autoregressive and moving average (ARMA) terms, a set of regressors, and a link function. We perform the model’s parameter estimation using the conditional maximum likelihood method. Closed-form expressions for the score vector and observed information matrix are presented. We propose and discuss techniques of diagnostic and forecasting for the new model. A Monte Carlo simulation study is carried out to evaluate the finite sample performance of the conditional maximum likelihood estimator. Finally, the proportion of stored hydroelectric energy in Northern Brazil is analyzed through the proposed model. The results evidence that the introduced RUBXII-ARMA model is suitable for describing the dynamics of the data and provides more accurate forecasts for the proportion of stored energy in Northern Brazil than those from competitors’ models.