A rapidly growing literature has documented important improvements in volatility measurement and forecasting performance through the use of realized volatilities constructed from high-frequency returns coupled with relatively simple reduced-form time series modeling procedures. Building on...

We propose a new decomposition of the realized covariance matrix into components based on the signs of the underlying high-frequency returns. Under an asymptotic setting in which the sampling interval goes to zero, we derive the asymptotic properties of the resulting realized semicovariance...