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arXiv · 2203.03237

Sequential Gaussian approximation for nonstationary time series in high dimensions

Fabian Mies·Ansgar Steland
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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.

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Fabian Mies, Ansgar Steland. 2022-03-07. Sequential Gaussian approximation for nonstationary time series in high dimensions. https://arxiv.org/abs/2203.03237

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