## Detail publikace

### Kristoufek, L.: Can the bivariate Hurst exponent be higher than an average of the separate Hurst exponents?

Autor: prof. PhDr. Ladislav Krištoufek Ph.D., Články v impaktovaných časopisech 2015 0 Physica A: Statistical Mechanics and Its Applications 431, pp. 124-127 arXiv PDF correlations, power-law cross-correlations, bivariate Hurst exponent, spectrum coherence GAČR 14-11402P Analýza dvoudimenzionální dlouhé paměti ve finančních časových řadách (2014-2016) GAUK 1110213 Dlouhá paměť křížových korelací: Teorie, testy, odhady a aplikace (GAUK submitted) In this note, we investigate possible relationships between the bivariate Hurst exponent $H_{xy}$ and an average of the separate Hurst exponents $\frac{1}{2}(H_x+H_y)$. We show that two cases are well theoretically founded. These are the cases when $H_{xy}=\frac{1}{2}(H_x+H_y)$ and $H_{xy}<\frac{1}{2}(H_x+H_y)$. However, we show that the case of $H_{xy}>\frac{1}{2}(H_x+H_y)$ is not possible regardless of stationarity issues. Further discussion of the implications is provided as well together with a note on the finite sample effect.