Outlier Detection in Beta Autoregressive Moving Average Model

The beta autoregressive moving average (βARMA) models are a dynamic model based on beta regression, used to model time series that take values in the interval (0, 1) and exhibit serial dependence. However, the presence of outliers can affect parameter estimation and the quality of predictions. Effective detection of these observations is therefore essential to ensure the model’s reliability. In this paper, we propose four methods for detecting outliers in the βARMA model. Three of them are adaptations of methods initially developed for beta regression models to the βARMA model, which integrate Tukey’s boxplot and Pearson residuals. The fourth procedure combines the Pearson residuals with the modified Z-score. All four procedures are adapted to the time series context and account for the serial dependence between observations. The performance of the proposed methods is evaluated through a Monte Carlo simulation study. We illustrate their practical relevance by applying them to real proportional data. Then the four methods exhibit high robustness in identifying true outliers, while limiting errors in identifying inliers as outliers, across different rates, amplitudes of contamination and sample sizes.