From zero to hero: Realized partial (co)variances

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This paper proposes a generalization of the class of realized semivariance and semicovariance measures introduced by Barndorff-Nielsen et al. (2010) and Bollerslev et al. (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-of-sample 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.






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Bollerslev, T, MC Medeiros, AJ Patton and R Quaedvlieg (2021). From zero to hero: Realized partial (co)variances. Journal of Econometrics. 10.1016/j.jeconom.2021.04.013 Retrieved from

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Tim Bollerslev

Juanita and Clifton Kreps Distinguished Professor of Economics, in Trinity College of Arts and Sciences

Professor Bollerslev conducts research in the areas of time-series econometrics, financial econometrics, and empirical asset pricing finance. He is particularly well known for his developments of econometric models and procedures for analyzing and forecasting financial market volatility. Much of Bollerslev’s recent research has focused on the analysis of newly available high-frequency intraday, or tick-by-tick, financial data and so-called realized volatility measures, macroeconomic news announcement effects, and the pricing of volatility risk. Recent reviews of his work are available in the two Handbook chapters "Volatility and Correlation Forecasting” (with Torben G. Andersen, Peter Christoffersen and Francis X. Diebold), Handbook of Economic Forecasting, (eds. Graham Elliott, Clive W.J. Granger and Allan Timmermann), 2006, and "Parametric and Nonparametric Volatility Measurement” (with Torben G. Andersen and Francis X. Diebold), in Handbook of Financial Econometrics, (eds. Yacine Aït-Sahalia and Lars P. Hansen), 2009.


Andrew J. Patton

Zelter Family Distinguished Professor

Patton’s research interests lie in financial econometrics, with an emphasis on forecasting volatility and dependence, forecast evaluation methods, high frequency financial data, and the analysis of hedge funds and mutual funds. His research has appeared in a variety of academic journals, including the Journal of Finance, Journal of Financial Economics, Review of Financial Studies, Econometrica, Journal of Econometrics, and the Journal of the American Statistical Association. He has given hundreds of invited seminars around the world, at universities, central banks, and other institutions. A complete list of his current and past research is available at:

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