Non-parametric estimation for pure jump irregularly sampled or noisy Lévy processes
Article first published online: 7 JUN 2010
© 2010 The Authors. Journal compilation © 2010 VVS
Special Issue: Statistical Inference for Lévy Processes with Applications to Finance
Volume 64, Issue 3, pages 290–313, August 2010
How to Cite
Comte, F. and Genon-Catalot, V. (2010), Non-parametric estimation for pure jump irregularly sampled or noisy Lévy processes. Statistica Neerlandica, 64: 290–313. doi: 10.1111/j.1467-9574.2010.00462.x
- Issue published online: 16 JUL 2010
- Article first published online: 7 JUN 2010
- Received: October 2009. Revised: January 2010.
- adaptive nonparametric estimation;
- Lévy processes;
- high frequency–low frequency data;
- irregular sampling;
- noisy observations
In this paper, we study non-parametric estimation of the Lévy density for pure jump Lévy processes. We consider n discrete time observations that may be irregularly sampled or possibly corrupted by a small noise independent of the main process. The case of non-noisy observations with regular sampling interval has been studied by the authors in previous works which are the benchmark for the extensions proposed here. We study first the case of a regular sampling interval and noisy data, then the case of irregular sampling for non-noisy data. In each case, non adaptive and adaptive estimators are proposed and risk bounds are derived.