Spectral estimation of the fractional order of a Lévy process

Denis Belomestny

No 2009-021, SFB 649 Discussion Papers from Humboldt University Berlin, Collaborative Research Center 649: Economic Risk

Abstract: 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.

Keywords: regular Lévy processes; Blumenthal-Getoor index; semiparametric estimation (search for similar items in EconPapers)
JEL-codes: C12 C13 (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:sfb649:sfb649dp2009-021

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