From zero to hero: Realized partial (co)variances

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 partial (co)variances" allow for multiple thresholds with various locations, rather than the single fixed threshold of zero used in semi (co)variances. We adopt methods from machine learning to choose the thresholds to maximize the out-ofsample forecast performance of time series models based on realized partial (co)variances. We find that in low dimensional settings it is hard, but not impossible, to improve upon the simple fixed threshold of zero. In large dimensions, however, the zero threshold embedded in realized semi covariances emerges as a robust choice.