Estimation of ordinal pattern probabilities in fractional Brownian motion

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dc.creatorSinn, Mathieu
dc.creatorKeller, Karsten
dc.date2008-01-10
dc.date.accessioned2026-07-07T08:53:40Z
dc.date.available2026-07-07T08:53:40Z
dc.descriptionFor equidistant discretizations of fractional Brownian motion (fBm), the probabilities of ordinal patterns of order d=2 are monotonically related to the Hurst parameter H. By plugging the sample relative frequency of those patterns indicating changes between up and down into the monotonic relation to H, one obtains the Zero Crossing (ZC) estimator of the Hurst parameter which has found considerable attention in mathematical and applied research. In this paper, we generally discuss the estimation of ordinal pattern probabilities in fBm. As it turns out, according to the sufficiency principle, for ordinal patterns of order d=2 any reasonable estimator is an affine functional of the sample relative frequency of changes. We establish strong consistency of the estimators and show them to be asymptotically normal for H<3/4. Further, we derive confidence intervals for the Hurst parameter. Simulation studies show that the ZC estimator has larger variance but less bias than the HEAF estimator of the Hurst parameter.
dc.description24 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/0801.1598
dc.identifierhttp://arxiv.org/abs/0801.1598
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145701
dc.subjectProbability
dc.subjectStatistics Theory
dc.subject60G18; 62M99
dc.titleEstimation of ordinal pattern probabilities in fractional Brownian motion
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