On the Estimation of Integrated Volatility With Jumps and Microstructure Noise

Abstract

In this article, we propose a nonparametric procedure to estimate the integrated volatility of an Itô semimartingale in the presence of jumps and microstructure noise. The estimator is based on a combination of the preaveraging method and threshold technique, which serves to remove microstructure noise and jumps, respectively. The estimator is shown to work for both finite and infinite activity jumps. Furthermore, asymptotic properties of the proposed estimator, such as consistency and a central limit theorem, are established. Simulations results are given to evaluate the performance of the proposed method in comparison with other alternative methods.

KEY WORDS:

• Central limit theorem
• High frequency data
• Quadratic variation
• Semimartingale

ACKNOWLEDGMENTS

The authors thank the Editor and the Associate Editor for their very extensive and constructive suggestions which helped to improve this article considerably. Jing’s research is partially supported by Hong Kong RGC HKUST6019/10P, HKUST6019/12P, and HKUST6022/13P. Kong’s research is supported in part by National NSFC No.11201080 and in part by Humanity and Social Science Youth Foundation of Chinese Ministry of Education No. 12YJC910003. Liu want to thank the financial support from The Science and Technology Development Fund of Macau (No.078/2012/A3 and No.078/2013/A3).