Optimal Gaussian Approximation for Multiple Time Series

01/28/2020

∙

by   Sayar Karmakar, et al.

∙

0

∙

share

We obtain an optimal bound for a Gaussian approximation of a large class of vector-valued random processes. Our results provide a substantial generalization of earlier results that assume independence and/or stationarity. Based on the decay rate of the functional dependence measure, we quantify the error bound of the Gaussian approximation using the sample size n and the moment condition. Under the assumption of pth finite moment, with p>2, this can range from a worst case rate of n^1/2 to the best case rate of n^1/p.