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Analysis of long-range dependence in financial time series was one of theinitial steps of econophysics into the domain of mainstream finance andfinancial economics in the 1990s. Since then, many different financial serieshave been analyzed using the methods standardly used outside of finance todeliver some important stylized facts of the financial markets. In the late2000s, these methods have started being generalized to bivariate settings sothat the relationship between two series could be examined in more detail. Itwas then only a single step from bivariate long-range dependence towardsscale-specific correlations and regressions as well as power-law coherency as aunique relationship between power-law correlated series. Such rapid developmentin the field has brought some issues and challenges that need furtherdiscussion and attention. We shortly review the development and historicalsteps from long-range dependence to bivariate generalizations and connectedmethods, focus on its technical aspects and discuss problematic parts andchallenges for future directions in this specific subfield of econophysics.

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