ESTIMATION FOR LEVY PROCESSES FROM HIGH FREQUENCY DATA WITHIN A LONG TIME INTERVAL

• 成果类型: Article
• 署名作者: Comte, Fabienne; Genon-Catalot, Valentine
• 署名单位: Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/10-AOS856
• 发表日期: 2011
• 页码: 803-837
• 关键词: nonparametric-estimation

摘要

In this paper, we study nonparametric estimation of the Levy density for Levy 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 Levy density and to provide a bound for the global 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.