Real-time scheme for the volatility estimation in the presence of microstructure noise

We are concerned with the problem of estimating temporal values of the volatility in the situation that the observation of the price process is contaminated by high frequency noise due to micro structural causes of the system. For the case that there is no such noise, we have presented in the preceding article ([3]) a scheme that is simple enough but might work effectively in a real-time manner. The aim of the present note is to introduce a new scheme by making suitable modifications to the old scheme so that the new one still maintains the nice property of being a real-time estimator.