Ranking Multivariate GARCH Models by Problem Dimension: An Empirical Evaluation

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In the last 15 years, several Multivariate GARCH (MGARCH) models have appeared in the literature. Recent research has begun to examine MGARCH specifications in terms of their out-of-sample forecasting performance. In this paper, we provide an empirical comparison of a set of models, namely BEKK, DCC, Corrected DCC (cDCC) of Aeilli (2008), CCC, Exponentially Weighted Moving Average, and covariance shrinking, using historical data of 89 US equities. Our methods follow part of the approach described in Patton and Sheppard (2009), and the paper contributes to the literature in several directions. First, we consider a wide range of models, including the recent cDCC model and covariance shrinking. Second, we use a range of tests and approaches for direct and indirect model comparison, including the Weighted Likelihood Ratio test of Amisano and Giacomini (2007). Third, we examine how the model rankings are influenced by the cross-sectional dimension of the problem.
JEL codes: C32, C53, C52. The authors wish to thank the Editor, Associate Editor, two referees, Christian Hafner, Sébastien Laurent, Francesco Violante, Roberto Casarin, Tommaso Proietti, Gian Piero Aielli, Adelchi Azzalini, Riccardo Jack Lucchetti, Eduardo Rossi, Giovanni Urga, participants at seminars in Louvain-la-Neuve and Zurich, and participants at the Italian Statistical Society XLV Conference, Padova, June 2010, CFE10 conference, London, December 2010, and ICEEE conference, Pisa, January 2011, for helpful comments and suggestions. For financial support, the second author wishes to thank the Australian Research Council, National Science Council, Taiwan, and the Japan Society for the Promotion of Science.
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