Ranking multivariate GARCH models by problem dimension

In the last 15 years, several Multivariate GARCH (MGARCH) models have appeared in the literature. The two most widely known and used are the Scalar BEKK model of Engle and Kroner (1995) and Ding and Engle (2001), and the DCC model of Engle (2002). Some 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 MGARCH models, namely BEKK, DCC, Corrected DCC (cDCC) of Aeilli (2008), CCC of Bollerslev (1990), Exponentially Weighted Moving Average, and covariance shrinking of Ledoit and Wolf (2004), using the historical data of 89 US equities. Our methods follow some of the approach described in Patton and Sheppard (2009), and contribute 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.