Bibliography

(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.