Limit theorems in the context of multivariate long-range dependence - Dueker, Marie-Christine (Stochastic Processes and their Applications, 2020)
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.
CRIS-Team Scopus Importer:2023-04-20
Keywords: Functional central limit theorem; Linear processes; Long-range dependence; Multivariate time series; Operator self-similar processes; Sample autocovariances