Scalar BEKK and indirect DCC

The paper derives the scalar special case of the well-known BEKK (the acronym BEKK comes from Baba, Engle, Kraft, and Kroner) multivariate GARCH model using a multivariate extension of the random coefficient autoregressive (RCA) model. This representation establishes the relevant structural and asymptotic properties of the scalar BEKK model using the theoretical results available in the literature for general multivariate GARCH. Sufficient conditions for the (direct) DCC (Dynamic Conditional Correlation) model to be consistent with a scalar BEKK representation are established. Moreover, an indirect DCC model that is consistent with the scalar BEKK representation is obtained, and is compared with the direct DCC model using an empirical example. The paper shows, within an asset allocation and risk measurement framework, that the two models are similar in terms of providing parameter estimates and forecasting value-at-risk thresholds for equally weighted and minimum variance portfolios.