Central limit theorems of range-based estimators for diffusion models. Issue 24 (17th December 2019)

• Record Type: Journal Article
• Authors: Cai, Jingwei; Zhu, Quanxin; Chen, Ping; Mei, Xia
• Is Part Of: Communications in statistics. Volume 48:Issue 24(2019)
• Page Start: 5969
• Page End: 5984
• Publication Date: 2019-12-17
• Subjects: Range-based instantaneous volatility estimator -- Central limit theorem -- Convergence in probability -- High frequency data; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2018.1523432
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: In this article, we consider non parametric range-based estimation procedure for diffusion processes and propose a instantaneous volatility estimator. Under some weak conditions, we certify that the proposed estimator has convergence in probability. Adding some necessary conditions, we prove a central limit theorem. By inference, we reach a conclusion that, with high frequency data in hand, the proposed estimator is more precise than those pure realized instantaneous volatility ones. Numerical simulation illustrates the finite sample properties of the proposed estimator.