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

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.

Keywords:

• Autoregression
• multivariate forecast
• prediction interval
• resampling methods
• vector autoregression
• weighted likelihood

Acknowledgments

We thank an Associate Editor and two anonymous reviewers for their careful reading of our manuscript and valuable suggestions and comments, which have helped us produce an improved version of our manuscript. The second author acknowledges the financial support from a research grant at the College of Business and Economics at the Australian National University.

Disclosure statement

No potential conflict of interest was reported by the author(s).