On the long range dependence of time-changed mixed fractional Brownian motion model

TL;DR

This paper investigates the long-range dependence properties of a time-changed mixed fractional Brownian motion, showing that certain subordination processes induce long-range dependence across all Hurst parameters.

Contribution

It introduces a novel analysis of long-range dependence in mixed fractional Brownian motion time-changed by gamma and tempered stable subordinators.

Findings

Time-changed mixed fractional Brownian motion exhibits long-range dependence for all H in (0,1).

The study characterizes the effects of gamma and tempered stable subordinators on dependence properties.

Main properties of the process are derived with focus on dependence structure.

Abstract

A time-changed mixed fractional Brownian motion is an iterated process constructed as the superposition of mixed fractional Brownian motion and other process. In this paper we consider mixed fractional Brownian motion of parameters a, b and H\in(0, 1) time-changed by two processes, gamma and tempered stable subordinators. We present their main properties paying main attention to the long range dependence. We deduce that the fractional Brownian motion time-changed by gamma and tempered stable subordinators has long range dependence property for all H\in(0, 1).