Short-range dependent processes subordinated to the Gaussian may not be strong mixing

TL;DR

This paper investigates whether short-range dependent processes subordinated to Gaussian processes are necessarily strong mixing, revealing that long-range dependence in the Gaussian process can prevent strong mixing in the subordinated process.

Contribution

It demonstrates that SRD processes subordinated to Gaussian processes are not always strong mixing when the underlying Gaussian process exhibits long-range dependence.

Findings

SRD processes subordinated to Gaussian processes may lack strong mixing.

Long-range dependence in Gaussian processes affects the mixing properties of subordinated processes.

The paper clarifies the relationship between dependence structures in Gaussian and subordinated processes.

Abstract

There are all kinds of weak dependence. For example, strong mixing. Short-range dependence (SRD) is also a form of weak dependence. It occurs in the context of processes that are subordinated to the Gaussian. Is a SRD process strong mixing if the underlying Gaussian process is long-range dependent? We show that this is not necessarily the case.