Many ways exist to measure and model financial asset volatility. In principle, as the frequency of the data increases, the quality of forecasts should improve. Yet, there is no consensus about a "true" or "best" measure of volatility. In this paper we propose to jointly consider absolute daily...

This paper proposes a generalization of the class of realized semivariance and semicovariance measures introduced by Barndorff-Nielsen, Kinnebrock and Shephard (2010) and Bollerslev, Li, Patton and Quaedvlieg (2020a) to allow for a finer decomposition of realized (co)variances. The new "realized...

This paper proposes a generalization of the class of realized semivariance and semicovariance measures introduced by Barndorff-Nielsen, Kinnebrock and Shephard (2010) and Bollerslev, Li, Patton and Quaedvlieg (2020a) to allow for a finer decomposition of realized (co)variances. The new "realized...

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...