AR-sieve Bootstrap for High-dimensional Time Series

TL;DR

This paper introduces a novel AR-sieve bootstrap method for high-dimensional time series that uses factor modeling to effectively handle dimensionality and dependence, with proven asymptotic properties and demonstrated advantages.

Contribution

A new factor-based AR-sieve bootstrap approach that reduces dimensionality and captures temporal dependence in high-dimensional time series.

Findings

The method performs well in simulations for high-dimensional data.

Bootstrap confidence intervals are successfully applied to real particulate matter data.

Asymptotic properties are rigorously established.

Abstract

This paper proposes a new AR-sieve bootstrap approach to high-dimensional time series. The major challenge of classical bootstrap methods on high-dimensional time series is two-fold: curse of dimensionality and temporal dependence. To address such a difficulty, we utilize factor modeling to reduce dimension and capture temporal dependence simultaneously. A factor-based bootstrap procedure is constructed, which performs an AR-sieve bootstrap on the extracted low-dimensional common factor time series and then recovers the bootstrap samples for the original data from the factor model. Asymptotic properties for bootstrap mean statistics and extreme eigenvalues are established. Various simulation studies further demonstrate the advantages of the new AR-sieve bootstrap in high-dimensional scenarios. An empirical application on particulate matter (PM) concentration data is studied, where bootstrap confidence intervals for mean vectors and autocovariance matrices are provided.