You should try single GARCH for each time series and then correlating them with a Copula function. Worked better with me, since M-GARCH are quite demanding when you have more than 3 or 4 variables.

PREDICTIVE FUNCTION (MODEL) should be able to predict the future not explain only the past. All autoregressive families of regression is about past telling not about future predicting. what is the use of a function or family of functions that can confirm past volatility, i.e. it "was" volatile? Can the model answer the questions: (i) Will it be volatile? If so, when?

Hi Abdellah Kadiri , here some alternatives:

1) Copulas (as previously pointed out by Antonio)

2) MGARCH models (CCC, DCC, cDCC, BEKK, etc)

3) Multivarite RiskMetric methodology (see the 2006 version)

4) Dimension reduction techniques (PCA, Principal Volatility components, dynamic factor models)

Best