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Drift parameter estimation for fractional Ornstein-Uhlenbeck process of the second kind
Stockholm University, Faculty of Social Sciences, Department of Statistics.
2015 (English)In: Statistics (Berlin), ISSN 0233-1888, E-ISSN 1029-4910, Vol. 49, no 1, 1-18 p.Article in journal (Refereed) Published
Abstract [en]

The fractional Ornstein-Uhlenbeck process of the second kind (fOU(2)) is the solution of the Langevin equation <inline-graphic xmlns:xlink= xlink:href=gsta_a_863888_ilm0001.gif></inline-graphic> with driving noise <inline-graphic xmlns:xlink= xlink:href=gsta_a_863888_ilm0002.gif></inline-graphic> where B is a fractional Brownian motion with Hurst parameter H(0, 1). In this article, in the case H>1/2, we prove that the least-squares estimator <inline-graphic xmlns:xlink= xlink:href=gsta_a_863888_ilm0003.gif></inline-graphic> introduced in [Hu Y, Nualart D. Parameter estimation for fractional Ornstein-Uhlenbeck processes. Stat. Probab. Lett. 2010;80(11-12):1030-1038], provides a consistent estimator. Moreover, using central limit theorem for multiple Wiener integrals, we prove asymptotic normality of the estimator valid for the whole range H(1/2, 1).

Place, publisher, year, edition, pages
2015. Vol. 49, no 1, 1-18 p.
Keyword [en]
fractional Ornstein-Uhlenbeck processes, Malliavin calculus, Langevin equation, least-squares estimator, 60G22, 60H07, 62F12
National Category
URN: urn:nbn:se:su:diva-114748DOI: 10.1080/02331888.2013.863888ISI: 000348852300001OAI: diva2:794814


Available from: 2015-03-12 Created: 2015-03-09 Last updated: 2015-03-12Bibliographically approved

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Morlanes, Jose Igor
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