Abstrakt
We introduce a general framework of the Mixed-correlated ARFIMA (MC-ARFIMA) processes which allows for various specifications of univariate and bivariate long-term memory. Apart from a standard case when H-xy = 1/2(H-x + H-y), MC-ARFIMA also allows for processes with Hxy < 1/2(H-x + H-y) but also for long-range correlated processes which are either short-range cross-correlated or simply correlated.
The major contribution of MC-ARFIMA lies in the fact that the processes have well-defined asymptotic properties for H-x, Hy and Hxy, which are derived in the paper, so that the processes can be used in simulation studies comparing various estimators of the bivariate Hurst exponent H-xy. Moreover, the framework allows for modeling of processes which are found to have H-xy < 1/2 (H-x+ H-y). (C) 2013 Elsevier B.V.
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