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Power variation analysis of some integral long-memory processes. (English) Zbl 1136.60035
Benth, Fred Espen (ed.) et al., Stochastic analysis and applications. The Abel symposium 2005. Proceedings of the second Abel symposium, Oslo, Norway, July 29 – August 4, 2005, held in honor of Kiyosi Itô. Berlin: Springer (ISBN 978-3-540-70846-9/hbk). Abel Symposia 2, 219-234 (2007).
The author considers processes of the form $$Z_{t}=\int_{0}^{t}u_{s}dB_{s}^{H}$$, where $$B_{s}^{H}$$ is a fractional Brownian motion with Hurst parameter $$H>1/2$$, $$u$$ is a stochastic process with finite $$q$$-variation, $$q<\frac{1}{1-H}$$ and the integral is defined in the Riemann-Stieltjes sense. The paper makes use of the statistical tools developed by J. M. Corcuera, D. Nualart and J. H. C. Woerner [Bernoulli 12, 713–735 (2006; Zbl 1130.60058)] to give consistent estimators of $$H$$, when $$u$$ is known and when $$u$$ is unknown. Some examples with Spanish financial market data are considered, and the obtained results are compared with the results using the well known R/S analysis.
For the entire collection see [Zbl 1113.60006].

##### MSC:
 60H05 Stochastic integrals 62E20 Asymptotic distribution theory in statistics
##### Keywords:
long-memory processes; fractional Brownian motion