Model-free Bootstrap for a General Class of Stationary Time Series

TL;DR

This paper introduces a model-free bootstrap method for stationary time series, providing asymptotic validity for confidence and prediction intervals, and demonstrates its effectiveness through finite-sample experiments comparing it to existing methods.

Contribution

It develops a new model-free bootstrap approach for stationary time series with proven asymptotic validity for confidence and prediction intervals.

Findings

The bootstrap method is asymptotically valid for various statistics.

Finite-sample experiments show competitive performance.

The method outperforms some existing bootstrap techniques.

Abstract

A model-free bootstrap procedure for a general class of stationary time series is introduced. The theoretical framework is established, showing asymptotic validity of bootstrap confidence intervals for many statistics of interest. In addition, asymptotic validity of one-step ahead bootstrap prediction intervals is also demonstrated. Finite-sample experiments are conducted to empirically confirm the performance of the new method, and to compare with popular methods such as the block bootstrap and the autoregressive (AR)-sieve bootstrap.