Prediction Intervals in the Beta Autoregressive Moving Average Model
This work addresses the need for reliable uncertainty quantification in time series forecasting for bounded data, such as water levels, but it is incremental as it extends existing methods to a specific model.
The paper tackled the problem of generating prediction intervals for the beta autoregressive moving average model, which is used for forecasting variables bounded between 0 and 1, and found that the bias-corrected and acceleration (BCa) prediction interval performed best with lower coverage rate distortion and small average length in Monte Carlo simulations.
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.