Title: Nonparametric inference on Levy-driven Ornstein-Uhlenbeck processes
Authors: Daisuke Kurisu - Tokyo Institute of Technology (Japan) [presenting]
Abstract: Nonparametric inference is studied for a stationary Levy-driven Ornstein-Uhlenbeck (OU) process with a compound Poisson subordinator. We propose a new spectral estimator for the Levy measure of the Levy-driven OU process 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 Levy measure and propose a practical method for bandwidth selection.