# Limit theorems for multivariate long-range dependent processes

## TL;DR

This paper establishes functional central limit theorems for multivariate linear processes with mixed short- and long-range dependence, revealing complex limit processes including multivariate Brownian motion, operator fractional Brownian motion, and Rosenblatt processes.

## Contribution

It extends limit theorems to multivariate processes with mixed dependence structures, analyzing their asymptotic behavior and limit processes.

## Key findings

- Limit theorems for sample mean and autocovariances are derived.
- Limit processes include multivariate Brownian motion, operator fractional Brownian motion, and Rosenblatt processes.
- Special attention is given to mixed short- and long-range dependence cases.

## 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.