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Limit theorems in the context of multivariate long-range dependence

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  • Düker, Marie-Christine

Abstract

This article considers multivariate linear processes whose components are either short- or long-range dependent. The functional central limit theorems for the sample mean and the sample autocovariances for these processes are investigated, paying special attention to the mixed cases of short- and long-range dependent series. The resulting limit processes can involve multivariate Brownian motion marginals, operator fractional Brownian motions and matrix-valued versions of the so-called Rosenblatt process.

Suggested Citation

  • Düker, Marie-Christine, 2020. "Limit theorems in the context of multivariate long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5394-5425.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:9:p:5394-5425
    DOI: 10.1016/j.spa.2020.03.011
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    References listed on IDEAS

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    6. Lavancier, Frédéric & Philippe, Anne & Surgailis, Donatas, 2009. "Covariance function of vector self-similar processes," Statistics & Probability Letters, Elsevier, vol. 79(23), pages 2415-2421, December.
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