Estimating a multivariate L\'evy density based on discrete observations

Maximilian F. Steffen

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arXiv · 2305.14315

Estimating a multivariate L\'evy density based on discrete observations

Maximilian F. Steffen

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Abstract

Existing results for the estimation of the L\'evy measure are mostly limited to the onedimensional setting. We apply the spectral method to multidimensional L\'evy 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.

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Maximilian F. Steffen. 2023-05-23. Estimating a multivariate L\'evy density based on discrete observations. https://arxiv.org/abs/2305.14315

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