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Journal of Time Series Econometrics

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Constrained Hamiltonian Monte Carlo in BEKK GARCH with Targeting

Martin Burda
  • Corresponding author
  • Department of Economics, University of Toronto, 150 St. George St., Toronto, ON M5S 3G7, Canada; IES, Charles University, Prague, Czech Republic
  • Email:
Published Online: 2013-07-03 | DOI: https://doi.org/10.1515/jtse-2013-0013


The GARCH class of models for dynamic conditional covariances trades off flexibility with parameter parsimony. The unrestricted BEKK GARCH dominates its restricted scalar and diagonal versions in terms of model fit, but its parameter dimensionality increases quickly with the number of variables. Covariance targeting has been proposed as a way of reducing parameter dimensionality, but for the BEKK with targeting the imposition of positive definiteness on the conditional covariance matrices presents a significant challenge. In this article, we suggest an approach based on Constrained Hamiltonian Monte Carlo that can deal effectively both with the nonlinear constraints resulting from BEKK targeting and the complicated nature of the BEKK likelihood in relatively high dimensions. We perform a model comparison of the full BEKK and the BEKK with targeting, indicating that the latter dominates the former in terms of marginal likelihood. Thus, we show that the BEKK with targeting presents an effective way of reducing parameter dimensionality without compromising the model fit, unlike the scalar or diagonal BEKK. The model comparison is conducted in the context of an application concerning a multivariate dynamic volatility analysis of a foreign exchange rate returns portfolio.

Keywords: dynamic conditional covariances; Markov chain Monte Carlo

JEL Classification: C11; C15; C32; C63


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About the article

Published Online: 2013-07-03

Published in Print: 2015-01-01

Citation Information: Journal of Time Series Econometrics, ISSN (Online) 1941-1928, ISSN (Print) 2194-6507, DOI: https://doi.org/10.1515/jtse-2013-0013. Export Citation

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