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

Abstract

Given a discrete time sample $X_1,...X_n$ from a Lévy process $X=(X_t{)}_{t\ge 0}$ of a finite jump activity, we study the problem of nonparametric estimation of the characteristic triplet $(\gamma ,{\sigma }^2,\rho )$ corresponding to the process $X.$ Based on Fourier inversion and kernel smoothing, we propose estimators of $\gamma ,{\sigma }^2$ and $\rho$ and study their asymptotic behaviour. The obtained results include derivation of upper bounds on the mean square error of the estimators of $\gamma$ and ${\sigma }^2$ and an upper bound on the mean integrated square error of an estimator of $\rho .$

29 pages

References in corpus (5)

• A kernel type nonparametric density estimator for decompounding
• Nonparametric adaptive estimation for pure jump Lévy processes
• Nonparametric estimation of the characteristic triplet of a discretely observed Lévy process
• Nonparametric estimation for Levy processes with a view towards mathematical finance
• Nonparametric estimation for Lévy processes from low-frequency observations

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