Sequential Gaussian approximation for nonstationary time series in high dimensions

Bernoulli, vol. 29

Abstract

Gaussian couplings of partial sum processes are derived for the high-dimensional regime d=o(n1∕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 Institute of Statistics

   RWTH Aachen University

   Affiliation as printed

   Institute of Statistics, RWTH Aachen University, Wüllnerstr. 3, Aachen, Germany

2. Ansgar Steland Aachen Institute of Statistics

   RWTH Aachen University

   Affiliation as printed

   Institute of Statistics, RWTH Aachen University, Wüllnerstr. 3, Aachen, Germany