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Some popular multivariate GARCH models such as BEKK and DCC have been criticized for the nonexistence of the corresponding stochastic processes and (if I interpret that correctly) the following meaninglessness of the parameter estimates; see e.g. McAleer (2019a) and McAleer (2019b). I wonder what are some multivariate GARCH models that do not suffer from such problems and have been shown to be fundamentally sound. References would be appreciated.

According to two broad surveys (Bauwens et al, 2006; Silvennoinen & Teäsvirta, 2009) of multivariate GARCH models, there are plenty of candidates to choose from. I am interested in which ones among them, or among newer ones, I could use with a clean conscience (from the statistical perspective).

References:

Richard Hardy
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  • Has the same type of objection been made for univariate models in the extended "X"-GARCH family? – Michael Oct 16 '20 at 02:52
  • @Michael, I don't know. Has it? – Richard Hardy Oct 16 '20 at 05:49
  • Don't know...what about the other question---has the existence been explicitly shown for all the variations/extensions of GARCH? Does existence follow trivially from the model specification in all cases? – Michael Oct 16 '20 at 06:52
  • @Michael, I guess existence has not been shown for all variations of univariate GARCH, but at least for some models I expect it has been shown. Some capable French mathematicians like Francq and Zakoian have worked on GARCH models, I guess they were rigorous all the way. I am not quite on that level (to put it mildly) and have struggled with the intuitive understanding of existence: see ["What is meant by existence of a (discrete-time) stochastic process?"](https://stats.stackexchange.com/questions/407725). – Richard Hardy Oct 16 '20 at 07:40
  • Interesting that even the univariate case existence has not been fully addressed (so it seems). Will see if I could add couple examples to the other question at some point. – Michael Oct 16 '20 at 09:33
  • @Michael, that would be lovely! The less technical they will be, the easier to digest, I think. – Richard Hardy Oct 16 '20 at 09:38

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