论文标题
Beta自回归运动平均模型的预测间隔
Prediction Intervals in the Beta Autoregressive Moving Average Model
论文作者
论文摘要
在本文中，我们提出了Beta自回归移动平均模型的五个预测间隔。该模型适用于在间隔$（0,1）$中假设值的建模和预测变量。提出的两个预测间隔是基于近似值考虑了β分布的正态分布和分位功能。我们还考虑基于自举的预测间隔，即：（i）引导程序预测错误（BPE）间隔； （ii）偏置校正和加速度（BCA）预测间隔； （iii）基于两种不同的自举方案的引导程序预测值的分位数的百分位预测间隔。根据蒙特卡洛模拟评估了提出的预测间隔。 BCA预测间隔在评估的间隔中提供了最佳性能，显示出较低的覆盖率失真和较小的平均长度。我们应用了我们的方法来预测巴西圣保罗的Cantareira供水系统的水位。
In this paper, 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.
