Modeling the dynamics of large conditional heteroskedastic covariance matrices Many economic and financial time series exhibit time varying volatility. GARCH models are tools for forecasting and analyzing the dynamics of this volatility. The co movements in financial markets and financial assets around the globe have recently become the main area of interest of financial econometricians; hence multivariate GARCH models have been introduced in order to capture these co movements. A large variety of multivariate GARCH models exists in the financial world and each of these models has its advantages and limitations. An important goal in constructing multivariate GARCH models is to make them parsimonious enough without compromising their adequacy in real world applications. Another aspect is to ensure that the conditional covariance matrix is a positive definite one...