Estimating a multivariate Lévy density based on discrete observations

2023/05/23 by Maximilian F. Steffen, Steffen, Maximilian F.
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60G51 #62G05 #62G07 #62M15 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability and Risk Models #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2305.14315

openalex publication_date 2023/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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