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

Given a discrete time sample X1, . . .Xn from a Levy process X = (Xt)t_0 of a finite jump activity, we study the problem of nonparametric estimation of the characteristic triplet (¿, s2, ¿) corresponding to the process X. Based on Fourier inversion and kernel smoothing, we propose estimators of ¿, s2 and ¿ and study their asymptotic behaviour. The obtained results include derivation of upper bounds on the mean square error of the estimators of ¿ and s2 and an upper bound on the mean integrated square error of an estimator of ¿.