  Podobnik and Stanley recently proposed a novel framework, Detrended
Cross-Correlation Analysis, for the analysis of power-law cross-correlation
between two time-series, a phenomenon which occurs widely in physical,
geophysical, financial and numerous additional applications. While highly
promising in these important application domains, to date no rigorous or
efficient statistical test has been proposed which uses the information
provided by DCCA across time-scales for the presence of this power-law
cross-correlation. In this paper we fill this gap by proposing a method based
on DCCA for testing the hypothesis of power-law cross-correlation; the method
synthesizes the information generated by DCCA across time-scales and returns
conservative but practically relevant p-values for the null hypothesis of zero
correlation, which may be efficiently calculated in software. Thus our
proposals generate confidence estimates for a DCCA analysis in a fully
probabilistic fashion.
