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.

摘要

在本文中，我们为 beta 自回归移动平均模型提出了五个预测区间。该模型适合对假设区间 (0, 1) 内的变量进行建模和预测。所提出的两个预测区间基于考虑正态分布和 beta 分布的分位数函数的近似值。我们还考虑基于引导的预测区间，即：（i）引导预测误差（BPE）区间；(ii) 偏差校正和加速度 (BCa) 预测区间；(iii)基于两个不同自举方案的自举预测值的分位数的百分位预测区间。根据蒙特卡洛模拟评估所提出的预测区间。BCa 预测区间在评估区间中提供了最佳性能，显示出较低的覆盖率失真和较小的平均长度。我们应用我们的方法来预测巴西圣保罗坎塔雷拉供水系统的水位。