Mixed-correlated ARFIMA processes for power-law cross-correlations

TL;DR

This paper introduces the MC-ARFIMA framework, enabling flexible modeling of long-term memory and cross-correlations in bivariate processes, with well-defined asymptotic properties for simulation and analysis.

Contribution

The paper presents a novel MC-ARFIMA framework that generalizes existing models by allowing various long-term memory and cross-correlation structures with explicit asymptotic properties.

Findings

Defines asymptotic properties of MC-ARFIMA processes

Allows modeling of processes with different Hurst exponent relationships

Facilitates simulation studies for estimator comparison

Abstract

We introduce a general framework of the Mixed-correlated ARFIMA (MC-ARFIMA) processes which allows for various specifications of univariate and bivariate long-term memory. Apart from a standard case when $H_{xy}={1}{2}(H_x+H_y)$, MC-ARFIMA also allows for processes with $H_{xy}<{1}{2}(H_x+H_y)$ but also for long-range correlated processes which are either short-range cross-correlated or simply correlated. The major contribution of MC-ARFIMA lays in the fact that the processes have well-defined asymptotic properties for $H_x$, $H_y$ and $H_{xy}$, which are derived in the paper, so that the processes can be used in simulation studies comparing various estimators of the bivariate Hurst exponent $H_{xy}$. Moreover, the framework allows for modeling of processes which are found to have $H_{xy}<{1}{2}(H_x+H_y)$.