For non-stationary high-dimensional time series with short memory and light tails, normalized sums can be approximated by Gaussian vectors in Wasserstein distance and on all convex sets at nearly optimal rates.
, Chetverikov , Denis D
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Wasserstein and Convex Gaussian Approximations for Non-stationary Time Series of Diverging Dimensionality
For non-stationary high-dimensional time series with short memory and light tails, normalized sums can be approximated by Gaussian vectors in Wasserstein distance and on all convex sets at nearly optimal rates.