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 H-xy and an average of the separate Hurst exponents 1/2 (H-x+H-y). We show that two cases are well theoretically founded. These are the cases when H-xy = 1/2 (H-x+H-y) and H-xy < 1/2 (H-x+H-y). However, we show that the case of H-xy > 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. (C) 2015 Elsevier B.V. All rights reserved.