Nonparametric inference on Lévy measures of compound Poisson-driven Ornstein-Uhlenbeck processes under macroscopic discrete observations

Abstract

This study examines a nonparametric inference on a stationary Lévy-driven Ornstein-Uhlenbeck (OU) process $X=(X_t{)}_{t\ge 0}$ 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 also derive, for the estimator, multivariate central limit theorems over a finite number of design points, and high-dimensional central limit theorems in the case wherein the number of design points increases with an increase in the sample size. Built on these asymptotic results, we develop methods to construct confidence bands for the Lévy measure and propose a practical method for bandwidth selection.

arXiv comment42 pages

References in corpus (13)

• Improving Point and Interval Estimates of Monotone Functions by Rearrangement
• A kernel type nonparametric density estimator for decompounding
• Nonparametric adaptive estimation for pure jump Lévy processes
• Nonparametric estimation of the characteristic triplet of a discretely observed Lévy process
• Statistical inference for time-changed Lévy processes via composite characteristic function estimation
• Nonparametric inference for discretely sampled Lévy processes
• Nonparametric inference on Lévy measures and copulas
• Efficient estimation of stable Levy process with symmetric jumps
• Efficient nonparametric inference for discretely observed compound Poisson processes
• Quantile estimation for Lévy measures
• Bootstrap confidence bands for spectral estimation of Lévy densities under high-frequency observations
• Adaptive nonparametric estimation for compound Poisson processes robust to the discrete-observation scheme
• An adaptive procedure for Fourier estimators: illustration to deconvolution and decompounding