Nonparametric inference on Lévy measures of Lévy-driven Ornstein-Uhlenbeck processes under discrete observations
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In this paper, we study nonparametric inference for a stationary Lévy-driven Ornstein-Uhlenbeck (OU) process X = (X_t)_t ≥ 0 with a compound Poisson subordinator. We propose a new spectral estimator for the Lévy measure of the Lévy-driven OU process X under macroscopic observations. We derive multivariate central limit theorems for the estimator over a finite number of design points. We also derive high-dimensional central limit theorems for the estimator in the case that the number of design points increases as the sample size increases. Building upon these asymptotic results, we develop methods to construct confidence bands for the Lévy measure.
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