Multivariate limit theorems in the context of long-range dependence

Murad S. Taqqu; Shuyang Bai

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arXiv · 1211.0576

Multivariate limit theorems in the context of long-range dependence

Murad S. Taqqu·Shuyang Bai

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Abstract

We study the limit law of a vector made up of normalized sums of functions of long-range dependent stationary Gaussian series. Depending on the memory parameter of the Gaussian series and on the Hermite ranks of the functions, the resulting limit law may be (a) a multivariate Gaussian process involving dependent Brownian motion marginals, or (b) a multivariate process involving dependent Hermite processes as marginals, or (c) a combination. We treat cases (a), (b) in general and case (c) when the Hermite components involve ranks 1 and 2. We include a conjecture about case (c) when the Hermite ranks are arbitrary.

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BibTeX RIS

Murad S. Taqqu, Shuyang Bai. 2013-04-11. Multivariate limit theorems in the context of long-range dependence. https://arxiv.org/abs/1211.0576

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