The purpose of the paper is to 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, provides the regularity conditions that arise from the underlying random coefficient autoregressive process, and 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, regularity conditions, and asymptotic properties of univariate and multivariate GARCH models. It is shown that the Full BEKK model, which in practice is estimated almost exclusively, has no underlying stochastic process, regularity conditions, or asymptotic properties.

Additional Metadata
Keywords Random coefficient stochastic process, Off-diagonal parametric restrictions, Diagonal and Full BEKK, Regularity conditions, Asymptotic properties, Conditional volatility, Univariate and multivariate models
JEL Time-Series Models; Dynamic Quantile Regressions (jel C22), Time-Series Models; Dynamic Quantile Regressions (jel C32), Model Evaluation and Testing (jel C52), Financial Econometrics (jel C58)
Persistent URL hdl.handle.net/1765/99514
Series Tinbergen Institute Discussion Paper Series , Econometric Institute Research Papers
Citation
Chang, C-L, & McAleer, M.J. (2017). The Fiction of Full BEKK (No. EI2017-05). Econometric Institute Research Papers. Retrieved from http://hdl.handle.net/1765/99514