Estimating a multivariate Lévy density based on discrete observations

05/23/2023

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by   Maximilian F. Steffen, et al.

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Existing results for the estimation of the Lévy measure are mostly limited to the onedimensional setting. We apply the spectral method to multidimensional Lévy processes in order to construct a nonparametric estimator for the multivariate jump distribution. We prove convergence rates for the uniform estimation error under both a low- and a high-frequency observation regime. The method is robust to various dependence structures. Along the way, we present a uniform risk bound for the multivariate empirical characteristic function and its partial derivatives. The method is illustrated with simulation examples.