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

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 to construct an adaptive nonparametric estimator and to provide a bound for the global ${\mathbb L}^2$-risk. Second, we use a direct approach (``time domain") which allows to construct an estimator on a given compact interval. We provide a bound for ${\mathbb L}^2$-risk restricted to the compact interval. We discuss rates of convergence and give examples and simulation results for processes fitting in our framework.
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Stochastic Processes and their Applications, Elsevier, 2009, 119 (12), pp.4088-4123. <10.1016/j.spa.2009.09.013>
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Dernière modification le : mardi 11 octobre 2016 - 11:57:16
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Fabienne Comte, Valentine Genon-Catalot. Nonparametric estimation for pure jump Lévy processes based on high frequency data.. Stochastic Processes and their Applications, Elsevier, 2009, 119 (12), pp.4088-4123. <10.1016/j.spa.2009.09.013>. <hal-00358184>

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