Generalized [formula omitted]ARMA model for double bounded time series forecasting

Abstract

The βARMA model is tailored for use with time series that assume values in (0,1). We generalize the model in which both the conditional mean and conditional precision evolve over time. The standard βARMA model, in which precision is constant, is a particular case of our model. The more general model formulation includes a parsimonious submodel for the precision parameter. We present the model conditional log-likelihood function, the conditional score function, and the conditional Fisher information matrix. We use the proposed model to forecast future levels of stored hydroelectric energy and the useful volume of a water reservoir in the South of Brazil. Our results show that more accurate forecasts are typically obtained by allowing the precision parameter to evolve over time.