New HEAVY Models for Fat-Tailed Realized Covariances and Returns

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

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

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
Volume36
Issue number4
DOIs
Publication statusPublished - 2 Oct 2018

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Covariance matrix
Volatility
F distribution
Positive Definiteness
simulation
Model
t-distribution
Equity
Stationarity
Outlier
equity
High-dimensional
Simulation Study
Filter
Restriction
Unknown
Formulation
Simulation
student
Observation

Keywords

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

Cite this

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title = "New HEAVY Models for Fat-Tailed Realized Covariances and Returns",
abstract = "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.",
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New HEAVY Models for Fat-Tailed Realized Covariances and Returns. / Opschoor, Anne; Janus, Pawel; Lucas, André; Van Dijk, Dick.

In: Journal of Business and Economic Statistics, Vol. 36, No. 4, 36, 02.10.2018, p. 643-657.

Research output: Contribution to JournalArticleAcademicpeer-review

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AU - Van Dijk, Dick

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