On the interplay between short and long term memory in the power-law cross-correlations setting

TL;DR

This paper investigates how short and long-term memory processes interact to produce power-law cross-correlations, revealing that correlated errors lead to predictable cross-correlation decay and that short-term memory strength does not affect asymptotic behavior.

Contribution

It demonstrates that power-law cross-correlations naturally emerge from processes with both short and long-term memory, especially when error terms are correlated, and clarifies the role of the bivariate Hurst exponent.

Findings

Power-law cross-correlations arise from correlated error terms.

The bivariate Hurst exponent equals the average of individual exponents.

Short-term memory strength does not influence asymptotic cross-correlation properties.

Abstract

We focus on emergence of the power-law cross-correlations from processes with both short and long term memory properties. In the case of correlated error-terms, the power-law decay of the cross-correlation function comes automatically with the characteristics of separate processes. Bivariate Hurst exponent is then equal to an average of separate Hurst exponents of the analyzed processes. Strength of short term memory has no effect on these asymptotic properties. Implications of these findings for the power-law cross-correlations concept are further discussed.