NONPARAMETRIC INFERENCE ON LEVY MEASURES AND COPULAS

• 成果类型: Article
• 署名作者: Buecher, Axel; Vetter, Mathias
• 署名单位: Ruhr University Bochum
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/13-AOS1116
• 发表日期: 2013
• 页码: 1485-1515
• 关键词: power variations; LIMIT-THEOREMS; dependence; asymptotics

摘要

In this paper nonparametric methods to assess the multivariate Levy measure are introduced. Starting from high-frequency observations of a Levy process X, we construct estimators for its tail integrals and the Pareto-Levy copula and prove weak convergence of these estimators in certain function spaces. Given n observations of increments over intervals of length Delta(n), the rate of convergence is k(n)(-1/2) for k(n) = n Delta(n) which is natural concerning inference on the Levy measure. Besides extensions to nonequidistant sampling schemes analytic properties of the Pareto-Levy copula which, to the best of our knowledge, have not been mentioned before in the literature are provided as well. We conclude with a short simulation study on the performance of our estimators and apply them to real data.