Nonparametric estimation of the characteristic triplet of a discretely observed Lévy process

Shota Gugushvili

Journal of Nonparametric Statistics, 2009, vol. 21, issue 3, 321-343

Abstract: Given a discrete time sample X1, … Xn from a Lévy process X=(Xt)t≥0 of a finite jump activity, we study the problem of nonparametric estimation of the characteristic triplet (γ, σ2, ρ) corresponding to the process X. Based on Fourier inversion and kernel smoothing, we propose estimators of γ, σ2 and ρ and study their asymptotic behaviour. The obtained results include derivation of upper bounds on the mean square error of the estimators of γ and σ2 and an upper bound on the mean integrated square error of an estimator of ρ.

Date: 2009
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Citations: View citations in EconPapers (19)

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DOI: 10.1080/10485250802645824

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