Nonparametric estimation of the local Hurst function of multifractional Gaussian processes |
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Authors: | Jean-Marc Bardet Donatas Surgailis |
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Institution: | 1. SAMM, Université de Paris 1, 90, rue de Tolbiac, 75634, Paris, France;2. Institute of Mathematics and Informatics, Vilnius, Lithuania |
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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. |
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Keywords: | primary 62G05 secondary 62G20 60F05 60G22 |
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