Do We Really Need Both BEKK and DCC? A Tale of Two Covariance Models

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Oil price shocks and stock market returns: New evidence from the United States and China (2014, background): “Additional useful discussion on the relationships between DCC and BEKK functional forms can also be found in Ding and Engle (2001), notwithstanding the important discussions already alluded to in Caporin and McAleer (2008, 2011) among others.”
Conditional correlations and volatility spillovers between crude oil and stock index returns (2010, unknown): “These models assume constant conditional correlations, and do not suffer from the curse of dimensionality, as compared with the VECH and BEKK models (see McAleer et al. (2008) and Caporin and McAleer (2009) for further details).”
Time-varying correlation between oil and stock market volatilities: Evidence from oil-importing and oil-exporting countries (2016, background): “More specifically, they base their argument on two papers by Caporin and McAleer (2008, 2012) who reveal that DCC does not deliver an accurate dynamic correlation, as opposed to the BEKK model that it does.”
Dynamic spillovers among major energy and cereal commodity prices (2014, background): “Caporin and McAleer (2009) show many similarities and dissimilarities between the BEKK and DCC models.”
Precious Metals-Exchange Rate Volatility Transmissions and Hedging Strategies (2009, unknown): “13 See Hamilton (2000) for a closer relationship between gold and platinum.”