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Multi-dimensional normal approximation of heavy-tailed moving averages

Author

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  • Azmoodeh, Ehsan
  • Ljungdahl, Mathias Mørck
  • Thäle, Christoph

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.

Suggested Citation

  • Azmoodeh, Ehsan & Ljungdahl, Mathias Mørck & Thäle, Christoph, 2022. "Multi-dimensional normal approximation of heavy-tailed moving averages," Stochastic Processes and their Applications, Elsevier, vol. 145(C), pages 308-334.
    • Handle: RePEc:eee:spapps:v:145:y:2022:i:c:p:308-334
    DOI: 10.1016/j.spa.2021.11.011
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    References listed on IDEAS

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    1. Mathias Mørck Ljungdahl & Mark Podolskij, 2020. "A minimal contrast estimator for the linear fractional stable motion," Statistical Inference for Stochastic Processes, Springer, vol. 23(2), pages 381-413, July.
    2. Nualart,David & Nualart,Eulalia, 2018. "Introduction to Malliavin Calculus," Cambridge Books, Cambridge University Press, number 9781107039124.
    3. Nualart,David & Nualart,Eulalia, 2018. "Introduction to Malliavin Calculus," Cambridge Books, Cambridge University Press, number 9781107611986.
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