  We investigate how simultaneously recorded long-range power-law correlated
multi-variate signals cross-correlate. To this end we introduce a two-component
ARFIMA stochastic process and a two-component FIARCH process to generate
coupled fractal signals with long-range power-law correlations which are at the
same time long-range cross-correlated. We study how the degree of
cross-correlations between these signals depends on the scaling exponents
characterizing the fractal correlations in each signal and on the coupling
between the signals. Our findings have relevance when studying parallel outputs
of multiple-component of physical, physiological and social systems.
