On the interplay between short and long term memory in the power-law cross-correlations setting

• Short and long term memory effects are studied in the power-law cross-correlations setting.
• Power-law cross-correlations emerge from memory properties of the separate processes.
• Strength of short term memory has no qualitative influence of these results.
• Implications for empirical analyses are discussed.

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.