  We focus on emergence of the power-law cross-correlations from processes with
both short and long term memory properties. In the case of correlated
error-terms, the power-law decay of the cross-correlation function comes
automatically with the characteristics of separate processes. Bivariate Hurst
exponent is then equal to an average of separate Hurst exponents of the
analyzed processes. Strength of short term memory has no effect on these
asymptotic properties. Implications of these findings for the power-law
cross-correlations concept are further discussed.
