Robust bootstrap prediction intervals for univariate and multivariate autoregressive time series models

TL;DR

This paper introduces a robust bootstrap method for constructing prediction intervals in univariate and multivariate autoregressive time series models, effectively handling outliers to improve forecast accuracy.

Contribution

It develops a novel robust bootstrap algorithm using weighted likelihood estimates and residuals, enhancing prediction interval reliability in the presence of outliers.

Findings

Improved forecast interval coverage in outlier-prone data

Robust method outperforms non-robust in simulations

Effective in real econometric data examples

Abstract

The bootstrap procedure has emerged as a general framework to construct prediction intervals for future observations in autoregressive time series models. Such models with outlying data points are standard in real data applications, especially in the field of econometrics. These outlying data points tend to produce high forecast errors, which reduce the forecasting performances of the existing bootstrap prediction intervals calculated based on non-robust estimators. In the univariate and multivariate autoregressive time series, we propose a robust bootstrap algorithm for constructing prediction intervals and forecast regions. The proposed procedure is based on the weighted likelihood estimates and weighted residuals. Its finite sample properties are examined via a series of Monte Carlo studies and two empirical data examples.