Can the bivariate Hurst exponent be higher than an average of the separate Hurst exponents

In this note, we investigate possible relationships between the bivariate Hurst exponent Hxy and an average of the separate Hurst exponents 12(Hx+Hy). We show that two cases are well theoretically founded. These are the cases when Hxy=12(Hx+Hy) and Hxy 12(Hx+Hy) 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.

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