New HEAVY Models for Fat-Tailed Realized Covariances and Returns

Anne Opschoor*, Pawel Janus, André Lucas, Dick Van Dijk

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


We develop a new score-driven model for the joint dynamics of fat-tailed realized covariance matrix observations and daily returns. The score dynamics for the unobserved true covariance matrix are robust to outliers and incidental large observations in both types of data by assuming a matrix-F distribution for the realized covariance measures and a multivariate Student's t distribution for the daily returns. The filter for the unknown covariance matrix has a computationally efficient matrix formulation, which proves beneficial for estimation and simulation purposes. We formulate parameter restrictions for stationarity and positive definiteness. Our simulation study shows that the new model is able to deal with high-dimensional settings (50 or more) and captures unobserved volatility dynamics even if the model is misspecified. We provide an empirical application to daily equity returns and realized covariance matrices up to 30 dimensions. The model statistically and economically outperforms competing multivariate volatility models out-of-sample. Supplementary materials for this article are available online.

Original languageEnglish
Article number36
Pages (from-to)643-657
Number of pages15
JournalJournal of Business and Economic Statistics
Issue number4
Publication statusPublished - 2 Oct 2018


  • Generalized autoregressive score (GAS) dynamics
  • Heavy tails
  • Matrix-F distribution
  • Multivariate volatility


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