Prediction Intervals in the Beta Autoregressive Moving Average Model

TL;DR

This paper introduces five new prediction intervals for the beta autoregressive moving average model, enhancing forecasting accuracy for variables in (0,1) with practical applications demonstrated on water level data.

Contribution

The paper develops and compares five novel prediction intervals for the beta ARMA model, including bootstrap-based methods, with the BCa interval showing superior performance.

Findings

BCa prediction interval had the best coverage and shortest average length.

Proposed intervals effectively forecast variables in (0,1).

Method validated through Monte Carlo simulations and real data application.

Abstract

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 S\~ao Paulo, Brazil.