A suggestion for constructing a large time-varying conditional covariance matrix

The construction of large conditional covariance matrices has posed a problem in the empirical literature because the direct extension of the univariate GARCH model to a multivariate setting produces large numbers of parameters to be estimated as the number of equations rises. A number of procedures have previously aimed to simplify the model and restrict the number of parameters, but these procedures typically involve either invalid or undesirable restrictions. This paper suggests an alternative way forward, based on the GARCH approach, which allows conditional covariance matrices of unlimited size to be constructed. The procedure is computationally straightforward to implement. At no point in the procedure is it necessary to estimate anything other than a univariate GARCH model.