Journal Article

**serial: **Physica. A : Statistical Mechanics and its Applications vol.431, 1 (2015), p. 124-127

**project(s): **GP14-11402P, GA ČR

**keywords: **Correlations,
Power-law cross-correlations,
Bivariate Hurst exponent,
Spectrum coherence

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**abstract (eng): **

In this note, we investigate possible relationships between the bivariate Hurst exponent Hxy 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.

**RIV: **AH