DCCA cross-correlation coefficient differentiation: theoretical and practical approaches

Abstract

We propose in this paper to establish a well-defined relationship between αDFA (the long range auto-correlation exponent) and λDCCA (the long range cross-correlation exponent), respectively described by the DFA and DCCA methods. This relationship will be accomplished theoretically by differentiating the DCCA cross-correlation coefficient, ρDCCA(n). Also, for some specific times series, we apply this theory in order to establish its validity.