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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].

60H05 Stochastic integrals
62E20 Asymptotic distribution theory in statistics