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

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

2008-07-22

arxiv.org/abs/0807.3469v2

Mathematics

Statistics Theory

29 pages

Scientific paper

Given a discrete time sample $X_1,... X_n$ from a L\'evy process $X=(X_t)_{t\geq 0}$ 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 $\rho.$

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