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Limit theorems in the context of multivariate long-range dependence |
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| Institution: | 1. University of Illinois, Urbana-Champaign, USA;2. Humboldt-Universität zu Berlin, Germany;1. Department of Physics, Indian Institute of Technology Kanpur, Kanpur, UP 208016, India;2. Samtel Center for Display Technologies, Indian Institute of Technology Kanpur, Kanpur, UP 208016, India;3. Materials Science Programme, Indian Institute of Technology Kanpur, Kanpur, UP 208016, India;1. Laboratoire de Mathématiques de Besançon, UMR CNRS 6623 Université de Franche-Comté, 16 route de Gray 25030, Besançon Cedex, France;2. Department of Mathematics, University of Alabama Birmingham, USA |
| 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. |
| Keywords: | Long-range dependence Multivariate time series Linear processes Sample autocovariances Functional central limit theorem Operator self-similar processes |
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