AR-sieve Bootstrap for High-dimensional Time Series

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.