  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.
