Estimation for Lévy processes from high frequency data within a long time interval

Details Estimation for Lévy processes from high frequency data within a long time interval Estimation for Lévy processes from high frequency data within a long time interval

2011-05-12

arxiv.org/abs/1105.2424v1

Annals of Statistics 2011, Vol. 39, No. 2, 803-837

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/10-AOS856 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/10-AOS856

In this paper, we study nonparametric estimation of the L\'{e}vy density for L\'{e}vy processes, with and without Brownian component. For this, we consider $n$ discrete time observations with step $\Delta$. The asymptotic framework is: $n$ tends to infinity, $\Delta=\Delta_n$ tends to zero while $n\Delta_n$ tends to infinity. We use a Fourier approach to construct an adaptive nonparametric estimator of the L\'{e}vy density and to provide a bound for the global ${\mathbb{L}}^2$-risk. Estimators of the drift and of the variance of the Gaussian component are also studied. We discuss rates of convergence and give examples and simulation results for processes fitting in our framework.

Affiliated with

Also associated with

No associations

Rating

Estimation for Lévy processes from high frequency data within a long time interval does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Estimation for Lévy processes from high frequency data within a long time interval, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Estimation for Lévy processes from high frequency data within a long time interval will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-496830