Journal Article

**serial: **Physica. A : Statistical Mechanics and its Applications vol.392, 24 (2013), p. 6484-6493

**project(s): **GA402/09/0965, GA ČR

**keywords: **power-law cross-correlations,
long-term memory,
econophysics

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**abstract (eng): **

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 $H_{xy} = /frac{1}{2}(H_x + H_y)$, MC-ARFIMA also allows for processes with $H_{xy} < /frac{1}{2}(H_x + H_y)$ 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 $H_{xy}$, which are derived in the paper, so that the processes can be used in simulation studies comparing various estimators of the bivariate Hurst exponent Hxy. Moreover, the framework allows for modeling of processes which are found to have $H_{xy} < /frac{1}{2}(H_x + H_y)$.

**RIV: **AH