Nonparametric estimation of the local Hurst function of multifractional Gaussian processes

Jean-Marc Bardet and Donatas Surgailis

Stochastic Processes and their Applications, 2013, vol. 123, issue 3, 1004-1045

Abstract: A new nonparametric estimator of the local Hurst function of a multifractional Gaussian process based on the increment ratio (IR) statistic is defined. In a general frame, the point-wise and uniform weak and strong consistency and a multidimensional central limit theorem for this estimator are established. Similar results are obtained for a refinement of the generalized quadratic variations (QV) estimator. The example of the multifractional Brownian motion is studied in detail. A simulation study is included showing that the IR-estimator is more accurate than the QV-estimator.

Keywords: Nonparametric estimators; Hurst function; Tangent process; Multifractional Brownian motion; Gaussian process; Central limit theorem (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (13)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:3:p:1004-1045

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DOI: 10.1016/j.spa.2012.11.009

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