We consider a new class of estimators for volatility functionals in the setting of frequently observed It¯o diffusions which are disturbed by i.i.d. noise. These statistics extend the approach of pre-averaging as a general method for the estimation of the integrated volatility in the presence...

The 2007-2008 global financial crisis and the subsequent anemic recovery have rekindled academic interest in quantifying the impact of uncertainty on macroeconomic dynamics based on the premise that uncertainty causes economic activity to slow down and contract. In this paper, we study the...