# Prediction Intervals in the Beta Autoregressive Moving Average Model

arXiv: https://arxiv.org/abs/2207.11628 · HTML: https://mlsanity.com/paper/2207.11628/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 70 references that are in the map.
- First posted on arXiv 24 Jul 2022.

## Builds on (most cited first, 5 of 5)

- [Bootstrap-based model selection criteria for beta regressions](https://mlsanity.com/paper/1405.4525/) (2014)
- [Beta seasonal autoregressive moving average models](https://mlsanity.com/paper/1806.07921/) (2018)
- [Kumaraswamy autoregressive moving average models for double bounded environmental data](https://mlsanity.com/paper/1710.05069/) (2017)
- [Beta Autoregressive Fractionally Integrated Moving Average Models](https://mlsanity.com/paper/1807.10338/) (2018)
- [A Dynamic Model for Double Bounded Time Series With Chaotic Driven Conditional Averages](https://mlsanity.com/paper/1902.09614/) (2019)

## Abstract (arXiv)

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.