Bootstrapping High Dimensional Time Series

Understand

This article studies bootstrap inference for high dimensional weakly dependent time series in a general framework of approximately linear statistics.

• The following high dimensional applications are covered: (1) uniform confidence band for mean vector; (2) specification testing on the second order property of time series such as white noise testing and bandedness testing of covariance matrix; (3) specification testing on the spectral property of time series.
• In theory, we first derive a Gaussian approximation result for the maximum of a sum of weakly dependent vectors, where the dimension of the vectors is allowed to be exponentially larger than the sample size.
• In particular, we illustrate an interesting interplay between dependence and dimensionality, and also discuss one type of "dimension free" dependence structure.