Power-law cross-correlations: Issues, solutions and future challenges

TL;DR

This paper reviews the evolution of methods analyzing power-law cross-correlations in financial time series, highlighting technical challenges and future research directions in the field of econophysics.

Contribution

It provides a comprehensive overview of the development from long-range dependence to bivariate and scale-specific correlation methods, emphasizing unresolved issues and future challenges.

Findings

Identification of technical issues in power-law cross-correlation analysis

Discussion of challenges in extending univariate methods to bivariate cases

Outline of future research directions in econophysics cross-correlation studies

Abstract

Analysis of long-range dependence in financial time series was one of the initial steps of econophysics into the domain of mainstream finance and financial economics in the 1990s. Since then, many different financial series have been analyzed using the methods standardly used outside of finance to deliver some important stylized facts of the financial markets. In the late 2000s, these methods have started being generalized to bivariate settings so that the relationship between two series could be examined in more detail. It was then only a single step from bivariate long-range dependence towards scale-specific correlations and regressions as well as power-law coherency as a unique relationship between power-law correlated series. Such rapid development in the field has brought some issues and challenges that need further discussion and attention. We shortly review the development and historical steps from long-range dependence to bivariate generalizations and connected methods, focus on its technical aspects and discuss problematic parts and challenges for future directions in this specific subfield of econophysics.