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 = (Xt) 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 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.

On the Uniform Convergence of Deconvolution Estimators From Repeated Measurements

“…Finally, we emphasize Lemma 1 could be applied to other contexts in econometrics and statistics. For example, it can be applied to examples discussed in Bonhomme and Robin (2010) and could also be used to extend the results in Kato and Kurisu (2020) and Kurisu (2019), which study nonparametric inference on univariate Lévy processes under high-and low-frequency observations, to multivariate setups.…”

On nonparametric inference for spatial regression models under domain expanding and infill asymptotics

“…. , N , N = N n → ∞ as n → ∞) by using techniques in those papers (see Kurisu (2018) for time series case). However, if we work with DEI asymptotics, to achieve such results would need careful treatment of the dependence among observations and the author believes that it requires substantial work.…”

“…, J, and let 0 < b 1 < · · · < b L and 0 < h 1 < · · · < h L be grids of bandwidths. We use a data-driven method which is similar to that proposed in Kurisu (2018).…”