Power variation of some integral fractional processes

Abstract

We consider the asymptotic behaviour of the realized power variation of processes of the form ∫ 0 t u s dB s H , where B H is a fractional Brownian motion with Hurst parameter H ∈(0,1) , and u is a process with finite q -variation, q <1/(1-H) . We establish the stable convergence of the corresponding fluctuations. These results provide new statistical tools to study and detect the long-memory effect and the Hurst parameter.

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