Multi-Dimensional Normal Approximation of Heavy-Tailed Moving Averages
Abstract
In this paper we extend the refined second-order Poincar\'e inequality for Poisson functionals from a one-dimensional to a multi-dimensional setting. Its proof is based on a multivariate version of the Malliavin-Stein method for normal approximation on Poisson spaces. We also present an application to partial sums of vector-valued functionals of heavy-tailed moving averages. The extension allows a functional with multivariate arguments, i.e. multiple moving averages and also multivariate values of the functional. Such a set-up has previously not been explored in the framework of stable moving average processes. It can potentially capture probabilistic properties which cannot be described solely by the one-dimensional marginals, but instead require the joint distribution.
Cite
@article{arxiv.2002.11335,
title = {Multi-Dimensional Normal Approximation of Heavy-Tailed Moving Averages},
author = {Ehsan Azmoodeh and Mathias Mørck Ljungdahl and Christoph Thäle},
journal= {arXiv preprint arXiv:2002.11335},
year = {2021}
}