Nonparametric estimation for pure jump Lévy processes based on high frequency data

F. Comte and V. Genon-Catalot

Stochastic Processes and their Applications, 2009, vol. 119, issue 12, 4088-4123

Abstract: In this paper, we study nonparametric estimation of the Lévy density for pure jump Lévy processes. We consider n discrete time observations with step [Delta]. The asymptotic framework is: n tends to infinity, [Delta]=[Delta]n tends to zero while n[Delta]n tends to infinity. First, we use a Fourier approach ("frequency domain"): this allows us to construct an adaptive nonparametric estimator and to provide a bound for the global -risk. Second, we use a direct approach ("time domain") which allows us to construct an estimator on a given compact interval. We provide a bound for -risk restricted to the compact interval. We discuss rates of convergence and give examples and simulation results for processes fitting in our framework.

Keywords: Adaptive; nonparametric; estimation; High; frequency; data; Lévy; processes; Projection; estimators (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (14)

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