Modeling long-range cross-correlations in two-component ARFIMA and FIARCH processes

TL;DR

This paper introduces two new stochastic models, ARFIMA and FIARCH, to generate and analyze long-range cross-correlated signals, revealing how their correlation depends on individual fractal properties and coupling strength.

Contribution

The paper presents novel two-component ARFIMA and FIARCH processes that model coupled fractal signals with long-range cross-correlations, advancing understanding of multivariate long-range dependence.

Findings

Cross-correlation degree depends on individual fractal exponents.

Coupling strength influences the level of cross-correlations.

Models are relevant for physical, physiological, and social systems.

Abstract

We investigate how simultaneously recorded long-range power-law correlated multi-variate signals cross-correlate. To this end we introduce a two-component ARFIMA stochastic process and a two-component FIARCH process to generate coupled fractal signals with long-range power-law correlations which are at the same time long-range cross-correlated. We study how the degree of cross-correlations between these signals depends on the scaling exponents characterizing the fractal correlations in each signal and on the coupling between the signals. Our findings have relevance when studying parallel outputs of multiple-component of physical, physiological and social systems.