## Publication detail

### Kristoufek, L.: Mixed-correlated ARFIMA processes for power-law cross-correlations

Author(s): prof. PhDr. Ladislav Krištoufek Ph.D., Articles in journals with impact factor 2013 0 Physica A: Statistical Mechanics and its Applications 392(24), pp. 6484-6493 arXiv PDF Power-law cross-correlations; Long-term memory; Econophysics 402/09/0965: New Approaches for monitoring and prediction of capital markets GACR P402/11/0948 Developing Analytical Framework for Energy Security: Time-Series Econometrics, Game Theory, Meta-Analysis and Theory of Regulation GAUK 1110213 Long-range cross-correlations: Theory, tests, estimators and application (GAUK submitted) SVV 267 504: Intensification of Doctoral Research in Economics and Finance: Extending Alternative Approaches to Economic Models 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 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 $H_{xy}<\frac{1}{2}(H_x+H_y)$.
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