Multivariate limit theorems in the context of long-range dependence
Files
Accepted manuscript
Date
2013-10-22
Authors
Taqqu, Murad S.
Bai, Shuyang
Version
Accepted manuscript
OA Version
Citation
Murad S Taqqu, Shuyang Bai. 2013. "Multivariate limit theorems in the context of long-range dependence." Journal of Time Series Analysis, Volume 34, Issue 6, pp. 717 - 743. https://doi.org/10.1111/jtsa.12046
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.