The purpose of the paper is to (i) show that univariate GARCH is not a special case of multivariate GARCH, specifically the Full BEKK model, except under parametric restrictions on the off-diagonal elements of the random coefficient autoregressive coefficient matrix, that are not consistent with Full BEKK, and (ii) provide the regularity conditions that arise from the underlying random coefficient autoregressive process, for which the (quasi-) maximum likelihood estimates have valid asymptotic properties under the appropriate parametric restrictions. The paper provides a discussion of the stochastic processes that lead to the alternative specifications, regularity conditions, and asymptotic properties of the univariate and multivariate GARCH models. It is shown that the Full BEKK model, which in empirical practice is estimated almost exclusively compared with Diagonal BEKK, has no underlying stochastic process that leads to its specification, regularity conditions, or asymptotic properties.

Asymptotic properties, Conditional volatility, Diagonal BEKK, Full BEKK, Off-diagonal parametric restrictions, Random coefficient stochastic process, Regularity conditions
22nd International Congress on Modelling and Simulation: Managing Cumulative Risks through Model-Based Processes, MODSIM 2017 - Held jointly with the 25th National Conference of the Australian Society for Operations Research and the DST Group led Defence Operations Research Symposium, DORS 2017
Erasmus School of Economics

Chang, C-L, & McAleer, M.J. (2017). The fiction of full BeKK. In Proceedings - 22nd International Congress on Modelling and Simulation, MODSIM 2017 (pp. 764–769). Retrieved from