Volatility Decomposition and Estimation in Time-Changed Price Models
  The usage of a spot volatility estimate based on a volatility decomposition in a time-changed price-model according to the trading times is investigated. In this model clock-time volatility splits up into the product of tick-time volatility and trading intensity, which both can be estimated from data and contain valuable information. By inspecting these two curves individually we gain more insight into the cause and structure of volatility. Several examples are provided where the tick-time volatility curve is much smoother than the clock-time volatility curve meaning that the major part of fluctuations in clock-time volatility is due to fluctuations of the trading intensity. Since microstructure noise only influences the estimation of the (smooth) tick-time volatility curve, the findings lead to an improved pre-averaging estimator of spot volatility. This is reflected by a better rate of convergence of the estimator. The asymptotic properties of the estimators are derived by an infill asymptotic approach. 
Rainer Dahlhaus and Sophon Tunyavetchakit
math.PR math.ST stat.TH