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 measures. The first-order asymptotic results highlight how the concordant components and the mixed-sign component load differently on economic information concerning stochastic correlation and jumps. The second-order asymptotics, taking the form of a novel non-central limit theorem, further reveals the fine structure underlying the concordant semicovariances, as manifest in the form of co-drifting and dynamic “leverage” type effects. In line with this anatomy, we empirically document distinct dynamic dependencies in the different realized semicovariance components based on data for a large cross-section of individual stocks. We further show that the accuracy of portfolio return variance forecasts may be significantly improved by using the realized semicovariance matrices to “look inside” the realized covariance matrices for signs of direction.

Additional Metadata
Keywords High-frequency data, realized variances, semicovariances, co-jumps, volatility forecasting.
JEL Time-Series Models; Dynamic Quantile Regressions (jel C22), Model Construction and Estimation (jel C51), Forecasting and Other Model Applications (jel C53), Financial Econometrics (jel C58)
Persistent URL hdl.handle.net/1765/124935
Journal Econometrica
Quaedvlieg, R, Bollerslev, T., Li, Jia, & Patton, A.J. (2020). Realized Semicovariances. Econometrica, In Press. Retrieved from http://hdl.handle.net/1765/124935