Estimating the Volatility Functionals with Multiple Transactions

The phenomenon of multiple transactions at each recording time is a common occurrence for high frequency financial data, due to heavy trading of the market and limitation of the recording mechanism. The situation has existed for a long time, but is getting more common in recent years due to heavier trading. Surprisingly, there has been hardly any study on this important issue, in spite of some ad hoc approaches to treat multiple transactions. In this paper we investigate how to handle multiple transactions, particularly in the context of estimating the integrated volatility and integrated quarticity, which are of great interest in financial econometrics. Two approaches are proposed for this purpose, and their asymptotic properties are investigated. Their performances are confirmed by simulation studies. The estimators are also applied to some real life problems. The work represents only the first step in this direction, and some future research problems are discussed