Prediction intervals in the beta autoregressive moving average model

Abstract

In this article, we propose five prediction intervals for the beta autoregressive moving average model. This model is suitable for modeling and forecasting variables that assume values in the interval (0, 1). Two of the proposed prediction intervals are based on approximations considering the normal distribution and the quantile function of the beta distribution. We also consider bootstrap-based prediction intervals, namely: (i) bootstrap prediction errors (BPE) interval; (ii) bias-corrected and acceleration (BCa) prediction interval; and (iii) percentile prediction interval based on the quantiles of the bootstrap-predicted values for two different bootstrapping schemes. The proposed prediction intervals were evaluated according to Monte Carlo simulations. The BCa prediction interval offered the best performance among the evaluated intervals, showing lower coverage rate distortion and small average length. We applied our methodology for predicting the water level of the Cantareira water supply system in São Paulo, Brazil.

Keywords:

• ARMA model
• Bootstrap
• Forecast
• Prediction intervals
• Time series

Additional information

Funding

We gratefully acknowledge partial financial support from Fundação de Amparo à Pesquisa do Estado do Rio Grande do Sul (FAPERGS), Conselho Nacional de Desenvolvimento Científico and Tecnológico (CNPq), and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Brazil.