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Power variation of some integral fractional processes
Corcuera, José Manuel Nualart, David Woerner, Jeannette H.C.
Corcuera, José Manuel
Nualart, David
Woerner, Jeannette H.C.
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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.
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This is the publisher's version, copyright by the Bernoulli Society for Mathematical Statistics and Probability.
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2006-08-01
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Bernoulli Society for Mathematical Statistics and Probability
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Corcuera, José Manuel; Nualart, David; Woerner, Jeannette H.C. (2006). "Power variation of some integral fractional processes." Bernoulli, 12(4):713-735.