TY - JOUR
T1 - Nonparametric estimation of the characteristic triplet of a discretely observed Lévy process
AU - Gugushvili, S.
PY - 2009
Y1 - 2009
N2 - Given a discrete time sample X1, … Xn from a L vy 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 ¿.
AB - Given a discrete time sample X1, … Xn from a L vy 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 ¿.
U2 - 10.1080/10485250802645824
DO - 10.1080/10485250802645824
M3 - Article
SN - 1048-5252
VL - 21
SP - 321
EP - 343
JO - Journal of Nonparametric Statistics
JF - Journal of Nonparametric Statistics
IS - 3
ER -