Sequential Gaussian approximation for nonstationary time series in high dimensions

RWTH Publications (RWTH Aachen)

Abstract

Gaussian couplings of partial sum processes are derived for the high-dimensional regime $d=o(n^{1/3})$. The coupling is derived for sums of independent random vectors and subsequently extended to nonstationary time series. Our inequalities depend explicitly on the dimension and on a measure of nonstationarity, and are thus also applicable to arrays of random vectors. To enable high-dimensional statistical inference, a feasible Gaussian approximation scheme is proposed. Applications to sequential testing and change-point detection are described.

Authors 2

1. Fabian Mies Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University , Germany

2. Ansgar Steland Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University , Germany