Power variation of some integral fractional processes

Abstract

We consider the asymptotic behaviour of the realized power variation of processes of the form ∫^(t)(0)u(s)dB^(H)(s), 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.