We do motivate why not other multivariate. Also need to motivate the multivariate t approach.
From Christoffersen:
Regime-switching models are arguably the main alternative to the DCC for modeling time-varying dependence we use in our analysis. For the use of regimeswitching models, see among others Ang and Bekaert (2002), Pelletier (2006), and Garcia and Tsafack (2011). In these models, each regime has a different level of dependence, and the choice of regime in each period is governed by an unobservable Markov chain. Asymmetric copulas such as the Clayton, Gumbel, or Joe-Clayton are difficult to generalize in higher dimension because they are defined with either one or two parameters. Chollete, Heinen, and Valdesogo (2009) recently proposed a regime-switching copula with two regimes in which one regime is characterized by a normal copula and the other by a canonical vine copula. Canonical vine copulas circumvent the dimensionality problem by assuming that the multivariate distribution can be decomposed into a hierarchy of bivariate functions. We estimate a model in which one regime is specified as a normal copula and the other as a t copula, and another model in which both regimes are characterized by t copulas. Note that in these two models, much modeling flexibility is gained because the second regime’s distribution is a series of t copulas, each having a different correlation and degree of freedom. Finally, we combine a normal copula with rotated Gumbel copulas. Such a specification is interesting because of its ability to capture asymmetry in dependence
We do motivate why not other multivariate. Also need to motivate the multivariate t approach.
From Christoffersen:
Regime-switching models are arguably the main alternative to the DCC for modeling time-varying dependence we use in our analysis. For the use of regimeswitching models, see among others Ang and Bekaert (2002), Pelletier (2006), and Garcia and Tsafack (2011). In these models, each regime has a different level of dependence, and the choice of regime in each period is governed by an unobservable Markov chain. Asymmetric copulas such as the Clayton, Gumbel, or Joe-Clayton are difficult to generalize in higher dimension because they are defined with either one or two parameters. Chollete, Heinen, and Valdesogo (2009) recently proposed a regime-switching copula with two regimes in which one regime is characterized by a normal copula and the other by a canonical vine copula. Canonical vine copulas circumvent the dimensionality problem by assuming that the multivariate distribution can be decomposed into a hierarchy of bivariate functions. We estimate a model in which one regime is specified as a normal copula and the other as a t copula, and another model in which both regimes are characterized by t copulas. Note that in these two models, much modeling flexibility is gained because the second regime’s distribution is a series of t copulas, each having a different correlation and degree of freedom. Finally, we combine a normal copula with rotated Gumbel copulas. Such a specification is interesting because of its ability to capture asymmetry in dependence