Nonparametric inference on Lévy measures and copulas
Loading...
Date
2012-05-03
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
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 n, the rate of convergence is k1=2
n for kn = nn
which is natural concerning inference on the Levy measure. 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.
Description
Table of contents
Keywords
copula, Levy copula, Levy measure, Levy process, nonparametric statistics, Pareto Levy copula, weak convergence