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Central limit theorems of range-based estimators for diffusion models

Author

Listed:
  • Jingwei Cai
  • Quanxin Zhu
  • Ping Chen
  • Xia Mei

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.

Suggested Citation

  • Jingwei Cai & Quanxin Zhu & Ping Chen & Xia Mei, 2019. "Central limit theorems of range-based estimators for diffusion models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(24), pages 5969-5984, December.
    • Handle: RePEc:taf:lstaxx:v:48:y:2019:i:24:p:5969-5984
    DOI: 10.1080/03610926.2018.1523432
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