  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 $H_{xy}={1}{2}(H_x+H_y)$,
MC-ARFIMA also allows for processes with $H_{xy}<{1}{2}(H_x+H_y)$ but also for
long-range correlated processes which are either short-range cross-correlated
or simply correlated. The major contribution of MC-ARFIMA lays in the fact that
the processes have well-defined asymptotic properties for $H_x$, $H_y$ and
$H_{xy}$, which are derived in the paper, so that the processes can be used in
simulation studies comparing various estimators of the bivariate Hurst exponent
$H_{xy}$. Moreover, the framework allows for modeling of processes which are
found to have $H_{xy}<{1}{2}(H_x+H_y)$.
