Nonparametric inference on L\'evy measures and copulas
Abstract
In this paper nonparametric methods to assess the multivariate L\'evy measure are introduced. Starting from high-frequency observations of a L\'evy process X, we construct estimators for its tail integrals and the Pareto-L\'evy 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 kn-1/2 for kn=nn which is natural concerning inference on the L\'evy measure. Besides extensions to nonequidistant sampling schemes analytic properties of the Pareto-L\'evy 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.
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