NON-PSD Coefficient Matrix in Diagonal BEKK

[kusdhianto]

I found that Diagonal VECH and Diagonal BEKK estimation produces exactly the same estimated coefficients. Referring to EViews User Guide II on page 454-456, the two models should be different. Furthermore, if the transformed matrix M in Eviews output is [Omega*Omega_inverse] matrix as in (31.58), then M must be at least positive semi definite (for example when M is restricted as diagonal matrix). However, I found the estimated matrix M is not always PSD.

Following is an example of the output

Covariance specification: Diagonal BEKK
GARCH = M + A1*RESID(-1)*RESID(-1)'*A1 + B1*GARCH(-1)*B1
M is a diagonal matrix*
A1 is a diagonal matrix
B1 is a diagonal matrix

Transformed Variance Coefficients

Coefficient Std. Error z-Statistic Prob.

M(1,1) 6.78E-07 1.73E-07 3.911068 0.0001
M(2,2) -1.73E-07 6.98E-09 -24.81260 0.0000
M(3,3) 7.32E-07 9.09E-08 8.050845 0.0000
M(4,4) 7.33E-07 1.29E-07 5.696765 0.0000
M(5,5) 4.89E-07 1.02E-07 4.808295 0.0000
M(6,6) 8.50E-07 1.67E-07 5.095860 0.0000
M(7,7) 2.08E-07 5.95E-08 3.496158 0.0005
M(8,8) 2.85E-06 9.67E-07 2.950033 0.0032
M(9,9) 1.88E-07 1.11E-07 1.690083 0.0910
M(10,10) 1.96E-07 1.30E-07 1.499435 0.1338
M(11,11) 1.76E-06 2.89E-07 6.079764 0.0000
M(12,12) 1.74E-07 6.04E-08 2.888401 0.0039

Does positive semi definiteness of M is assured in the diagonal BEKK in EViews?