# 16-061/III (2016-08-11)

Author(s)
Peter Reinhard Hansen, University of North Carolina at Chapel Hill, United States; Pawel Janus, UBS Global Asset Management, Zürich, Switzerland; Siem Jan Koopman, VU University Amsterdam, the Netherlands
Keywords:
high-frequency data, multivariate GARCH, multivariate volatility, realised covariance, score, Wishart density
JEL codes:
C32, C52, C58

We propose a novel multivariate GARCH model that incorporates realized measures for the variance matrix of returns. The key novelty is the joint formulation of a multivariate dynamic model for outer-products of returns, realized variances and realized covariances. The updating of the variance matrix relies on the score function of the joint likelihood function based on Gaussian and Wishart densities. The dynamic model is parsimonious while each innovation still impacts all elements of the variance matrix. Monte Carlo evidence for parameter estimation based on different small sample sizes is provided. We illustrate the model with an empirical application to a portfolio of 15 U.S. financial assets.