DCCA cross-correlation coefficient differentiation: Theoretical and practical approaches

We propose in this paper to establish a well-defined relationship between α D F A (the long range auto-correlation exponent) and λ D C C A (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, ρ D C C A ( n ) . Also, for some specific times series, we apply this theory in order to establish its validity.