Theoretical and Empirical Differences Between Diagonal and Full BEKK for Risk Management
The purpose of the paper is to explore the relative biases in the estimation of the Full BEKK model as compared with the Diagonal BEKK model, which is used as a theoretical and empirical benchmark. Chang and McAleer  show that univariate GARCH is not a special case of multivariate GARCH, specically, the Full BEKK model, and demonstrate that Full BEKK which, in practice, is estimated almost exclusively, has no underlying stochastic process, regularity conditions, or asymptotic properties. Diagonal BEKK (DBEKK) does not suf- fer from these limitations, and hence provides a suitable benchmark. We use simulated nancial returns series to contrast estimates of the conditional vari- ances and covariances from DBEKK and BEKK. The results of non-parametric tests suggest evidence of considerable bias in the Full BEKK estimates. The results of quantile regression analysis show there is a systematic relationship between the two sets of estimates as we move across the quantiles. Estimates of conditional variances from Full BEKK, relative to those from DBEKK, are lower in the left tail and higher in the right tail.
|Keywords||DBEKK, BEKK, Regularity Conditions, Asymptotic Properties, Non-Parametric, Bias, Qantile regression|
|JEL||Estimation (jel C13), Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions (jel C21), Financial Econometrics (jel C58)|
|Series||Tinbergen Institute Discussion Paper Series , Econometric Institute Research Papers|
Tan, A.C, & McAleer, M.J. (2017). Theoretical and Empirical Differences Between Diagonal and Full BEKK for Risk Management (No. EI2017-22). Econometric Institute Research Papers. Retrieved from http://hdl.handle.net/1765/101765