A structural GARCH model: An application on South African data

This paper proposes a two-step methodology to decompose the conditional covariance matrix of a system of financial variables for South Africa. This two-step approach allows one to identify the system, and determine the “endogenous” conditional covariance matrix as well as the “exogenous” conditional covariance matrix. The approach utilises two multivariate GARCH models to obtain the results. In the first step, a multivariate GARCH model developed by Rigobon and Sack [Rigobon, R and Sack, B, 2003. Spillovers Across U.S. Financial Markets. MIT, Mimeo.] is utilised. This model solves the identification problem using heteroscedasticity as instrument, while an estimate for the conditional covariance matrix of the external structural innovations can also be recovered from the model. The second step utilises a standard BEKK model. The BEKK specification is used to estimate the conditional covariance matrix of the “endogenous” variation from within the system. Once the two steps are completed, the conditional covariance matrices can be summed in order to get the conditional covariance matrix for the total system. The two-step methodology allows for analysis of the variances that is not possible with traditional multivariate GARCH models.