Copula-MGARCH with continuous covariance decomposition

- Continuous decomposition of the innovations' covariance matrix via rotations.
- Joint estimation via Maximum Likelihood and application to foreign exchange rates.
- In-sample and ex-ante tests show the benefits of the enhanced model flexibility.
- Further support for the hypothesis of higher order dependencies in innovations.

The Copula-MGARCH (C-MGARCH) model by Lee and Long (2009) incorporates standardized copula distributed innovations in MGARCH models. We motivate an extension of the C-MGARCH model by means of a continuous decomposition of the innovations' covariance matrix. An extended BEKK(1, 1) model with rotated standardized innovations is outlined for the bivariate case. The model parameters and the rotation angle are jointly estimated by means of Maximum Likelihood. We conduct an application to the log-differences of Euro/US-Dollar and Japanese Yen/US-Dollar daily exchange rates. In-sample information criteria and ex-ante portfolio Value-at-Risk coverage tests show that the enhanced flexibility of the rotated C-MGARCH is supported by the data.