Improved Sieve Bootstrap based prediction intervals for time series

Abstract

Forecasting future observations is one of the main goals of time series modeling. Point forecasts are the most common type of prediction, but interval predictions are more informative, usually obtained as prediction intervals (PIs). The conventional Box-Jenkins PIs perform well when the underlying distributional assumptions hold. To circumvent such adherence, resampling methods such as residual based Bootstrap were one of the approaches for constructing PIs, but these are only suitable when the order of the process is known. Sieve Bootstrap method has the advantage of requiring no such prior knowledge. In this work, two new Sieve Bootstrap methods have been proposed. The performance of the proposed methods for constructing PIs have been compared with the existing Bootstrap methods. One of the proposed methods, namely, predictive residual based rescaled Sieve Bootstrap (PRSB) has been found to outperform the other proposed predictive residual based Sieve Bootstrap (PSB) and also the existing methods considered. PSB method has been found to be superior to Box-Jenkins and existing Sieve Bootstrap methods. The proposed methods are not only an improvement over the existing predictive residual based Bootstrap methods in AR(p) set up but also have been extended to be applicable in ARMA(p, q) situations as well.

Keywords:

• Auto-regressive moving average (ARMA)
• Coverage probability
• Non-parametric method
• Predictive residual
• Resampling

Acknowledgements

The facilities provided by ICAR-Indian Agricultural Statistics Research Institute (IASRI), New Delhi and the funding granted to the first author by Indian Council of Agricultural Research in the form of IARI-SRF fellowship is duly acknowledged for carrying out this study, which is part of his doctoral research work being pursued at IASRI. Thanks are also due to the reviewer whose comments have improved the paper to a great extent.

Disclosure statement

No potential conflict of interest was reported by the authors.