Bootstrap confidence bands for spectral estimation of Levy densities under high-frequency observations

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Kato, Kengo¹  Kurisu, Daisuke² 

[1] Cornell Univ, Dept Stat & Data Sci, 1194 Comstock Hall, Ithaca, NY 14853 USA

[2] Tokyo Inst Technol, Sch Engn, Dept Ind Engn & Econ, Meguro Ku, 2-12-1 Ookayama, Tokyo 1528552, Japan

关键词: Empirical bootstrap;    High-frequency data;    Levy process;    Multiplier bootstrap;    Spectral estimation;   

DOI  :  10.1016/j.spa.2019.04.012

来源: Elsevier

【 摘 要 】

This paper develops bootstrap methods to construct uniform confidence bands for nonparametric spectral estimation of Levy densities under high-frequency observations. We are given n discrete observations at frequency 1/Delta, and assume that Delta = Delta(n) -> 0 and n Delta -> infinity as n -> infinity. We employ a spectral estimator of the Levy density, and develop novel implementations of multiplier and empirical bootstraps to construct confidence bands on a compact set away from the origin. We provide conditions under which the confidence bands are asymptotically valid. We also develop a practical method for bandwidth selection, and conduct numerical studies. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free