Multivariate Leverage Effects and Realized Semicovariance GARCH Models

Tim Bollerslev, Andrew J. Patton, Rogier Quaedvlieg

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We propose new asymmetric multivariate volatility models. The models exploit estimates of variances and covariances based on the signs of high-frequency returns, measures known as realized semivariances, semicovariances, and semicorrelations, to allow for more nuanced responses to positive and negative return shocks than threshold “leverage effect” terms traditionally used in the literature. Our empirical implementations of the new models, including extensions of widely-used bivariate GARCH specifications for a number of individual stocks and the aggregate market portfolio as well as larger dimensional dynamic conditional correlation type formulations for a cross-section of individual stocks, provide clear evidence of improved model fit and reveal new and interesting asymmetric joint dynamic dependencies.

Original languageEnglish
JournalJournal of Econometrics
Pages (from-to)411-430
Number of pages20
Publication statusPublished - 2020


  • Asymmetric dependence
  • High-frequency data
  • Realized correlation
  • Realized volatility
  • Semivariance


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