Limit theorems for multivariate long-range dependent processes

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.

References in corpus (4)

• Integral representations and properties of operator fractional Brownian motions
• Covariance function of vector self-similar process
• Invariance principle for stochastic processes with short memory
• The central limit theorem for a sequence of random processes with space varying long memory