Mixed-correlated ARFIMA processes for power-law cross-correlations

We introduce a general framework of the Mixed-correlated ARFIMA (MC-ARFIMA) processes which allows for various specifications of univariate and bivariate long-term memory. Apart from a standard case when H x y = 1 2 ( H x + H y ) , MC-ARFIMA also allows for processes with H x y < 1 2 ( H x + H y ) but also for long-range correlated processes which are either short-range cross-correlated or simply correlated. The major contribution of MC-ARFIMA lies in the fact that the processes have well-defined asymptotic properties for H x , H y and H x y , which are derived in the paper, so that the processes can be used in simulation studies comparing various estimators of the bivariate Hurst exponent H x y . Moreover, the framework allows for modeling of processes which are found to have H x y < 1 2 ( H x + H y ) .