Multi-dimensional normal approximation of heavy-tailed moving averages

Ehsan Azmoodeh, Mathias Mørck Ljungdahl and Christoph Thäle

Stochastic Processes and their Applications, 2022, vol. 145, issue C, 308-334

Abstract: In this paper we extend the refined second-order Poincaré 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.

Keywords: Central limit theorem; Heavy-tailed moving average; Lévy process; Malliavin–Stein method; Poisson random measure; Second-order Poincaré inequality (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2021.11.011

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