@MVGARCHTOVECH strips the GARCH parameters out of a just-estimated GARCH model and converts them to a standard VECH representation. The VECH representation has

 

\(\begin{array}{l} vech\,{{\bf{H}}_t} = {\bf{C}} + {\bf{B}}\,vech\,{{\bf{H}}_{t - 1}} + {\bf{A}}\,vech\left( {{{\bf{u}}_{t - 1}}{\bf{u}'_{t - 1}}} \right) + \bf{D}\,vech\left( {{{\bf{v}}_{t - 1}}{\bf{v}'_{t - 1}}} \right) \\ {{\bf{v}}_t} = \min ({{\bf{u}}_t},0) \\ \end{array}\)

The \({\bf{D}}\) is only present if you add the ASYMMETRIC option. vech takes a symmetric matrix and strings it out into a vector according to the rows of the lower triangle, that is, the components of a 3 variable model will be in the order

 

1

2 3

4 5 6

 

Note that starting with version 9, the GARCH instruction has the option VECHMAT which produces the same matrices. If you use VECHMAT=MYVECH, then MYVECH("A") will be the \({\bf{A}}\) matrix, MYVECH("C") will be the \({\bf{C}}\) vector, etc. 

 

@MVGARCHtoVECH( options )

Options

MV=[STANDARD]/BEKK/DIAGONAL/VECH

ASYMMETRIC/[NOASYMMETRIC]

These should repeat the options from the GARCH instruction. Note that several classes of models (such as CC and DCC) have no VECH representation.

Variables Defined

 

Copyright © 2025 Thomas A. Doan