Kernel Method for Realized Volatility Estimation Using High-Frequency Non-Equally Spaced Price Data

• Activity Number: 246
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Xiaoguang Wang*+ and Michael Levine and Jian Zou
• Companies: Purdue University and Purdue University and Indiana University-Purdue University Indianapolis
• Keywords: High frequency data ; realized volatility ; kernel method ; random trading times ; micro-structural noise ; functional central limit theory

Abstract

In our paper, we extend the realized kernel estimator (Barndorff-Nielsen, et al. 2008) of the realized volatility to the case of non-equally spaced high frequency data and derived several important theories which lay the foundation of the central limit theorem for the realized kernel estimator in this more general case. We further found a boundary case, in the sense that if the trading duration follows a distribution whose variance decreases faster than the square of its expectation as number of transactions go to infinity within a fixed time interval, then the randomness from the trading times can be ignored and the realized kernel estimator applied on the whole non-equally spaced price data will still have the same asymptotic properties as in the equally-spaced data case. Otherwise, the influence of the random trading time cannot be ignored and the estimator applied on the whole tick-by-tick data measures two resources of randomness, one from trading times, another one from the magnitude changes of price. Meanwhile, in this case, some adjustments on the realized kernel estimator should be made if it is supposed to only measure the magnitude variation of price changes.