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February 2010 Spectral estimation of the fractional order of a Lévy process
Denis Belomestny
Ann. Statist. 38(1): 317-351 (February 2010). DOI: 10.1214/09-AOS715


We consider the problem of estimating the fractional order of a Lévy process from low frequency historical and options data. An estimation methodology is developed which allows us to treat both estimation and calibration problems in a unified way. The corresponding procedure consists of two steps: the estimation of a conditional characteristic function and the weighted least squares estimation of the fractional order in spectral domain. While the second step is identical for both calibration and estimation, the first one depends on the problem at hand. Minimax rates of convergence for the fractional order estimate are derived, the asymptotic normality is proved and a data-driven algorithm based on aggregation is proposed. The performance of the estimator in both estimation and calibration setups is illustrated by a simulation study.


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Denis Belomestny. "Spectral estimation of the fractional order of a Lévy process." Ann. Statist. 38 (1) 317 - 351, February 2010.


Published: February 2010
First available in Project Euclid: 31 December 2009

zbMATH: 1181.62151
MathSciNet: MR2589324
Digital Object Identifier: 10.1214/09-AOS715

Primary: 62F10
Secondary: 62F25 , 62H12 , 62J12

Keywords: Blumenthal–Getoor index , Regular Lévy processes , Semiparametric estimation

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 1 • February 2010
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