We propose a decomposition of the realized covariance matrix into components based on the signs of the underlying high-frequency returns, and we derive the asymptotic properties of the resulting realized semicovariance measures as the sampling interval goes to zero. The first-order asymptotic results highlight how the same-sign and mixed-sign components load differently on economic information related to stochastic correlation and jumps. The second-order asymptotic results reveal the structure underlying the same-sign semicovariances, as manifested in the form of co-drifting and dynamic “leverage” effects. In line with this anatomy, we use data on a large cross-section of individual stocks to empirically document distinct dynamic dependencies in the different realized semicovariance components. We show that the accuracy of portfolio return variance forecasts may be significantly improved by exploiting the information in realized semicovariances.

Additional Metadata
Keywords co-jumps, High-frequency data, realized variances, semicovariances, 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 dx.doi.org/10.3982/ECTA17056, hdl.handle.net/1765/129249
Journal Econometrica
Bollerslev, T, Li, J. (Jia), Patton, A.J, & Quaedvlieg, R. (2020). Realized Semicovariances. Econometrica, 88(4), 1515–1551. doi:10.3982/ECTA17056