On Estimating the Integrated Co-Volatility Using Noisy High-Frequency Data with Jumps

Abstract

In this article, we consider the estimation of covariation of two asset prices which contain jumps and microstructure noise, based on high-frequency data. We propose a realized covariance estimator, which combines pre-averaging method to remove the microstructure noise and the threshold method to reduce the jumps effect. The asymptotic properties, such as consistency and asymptotic normality, are investigated. The estimator allows very general structure of jumps, for example, infinity activity or even infinity variation. Simulation is also included to illustrate the performance of the proposed procedure.

Keywords:

• Central limit theorem
• Co-volatility
• High-frequency data
• Ito semi-martingale
• Jumps
• Microstructure noise

Mathematics Subject Classification:

• Primary 60F05, 60F17
• Secondary 60G51, 60G07

Acknowledgments

The authors would like to thank the Editor, an Associate Edition, and two referees for their constructive suggestions that improved this article considerably. JING's research is supported by Hong Kong RGC grants HKUST6011/07P and HKUST6015/08P, and in part by Fundamental Research Funds for the Central Universities, and Research Funds of Renmin University of China (Grant No. 10XNL007) and by NSFC (Grant No. 71071155). Liu want to thank the financial support of NSFC (71171103), University of Macau (SRG023-FST12-LZ) and from The Science and Technology Development Fund of Macau Government (FDCT078/2012/A3).