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Abstract:
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We consider the problem of approximating sums of stationary as well as non-stationary time series by Gaussian vectors, using the framework of functional dependence measure. Both low and high dimensional settings will be discussed. The approximation errors are optimal for a large class of vector-valued random processes. Our results substantially generalize earlier ones which assume independence and/or stationarity. Based on the decay rate of functional dependence measure, we quantify the error bound of the Gaussian approximation based on the sample size n, the dimension p, and the moment conditions. This work is joint with Sayar Karmakar and Danna Zhang.
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