SVAR and MGARCH

[luxu1983]

dear
If i want to combine the SVAR and MGARCH model
How can i estimate svar and mgarch model at the same time
Thank you very much

[TomDoan]

How do you want to combine them? GARCH generates a time-varying model for the covariance matrix; SVAR generates a time-invariant model for the covariance matrix. There are models like triangular BEKK which restrict how the GARCH variances are built.

[luxu1983]

How do you want to combine them? GARCH generates a time-varying model for the covariance matrix; SVAR generates a time-invariant model for the covariance matrix. There are models like triangular BEKK which restrict how the GARCH variances are built.

my meaning is "let the mean equation as the SVAR model , and allow the structural residuals ε to follow a general GARCH process"
can i estimate them together using Max?

[TomDoan]

The VAR generates a standard VECT[SERIES] of residuals, call them u(t). Your SVAR maps u(t) to a VECT[SERIES] of structural residuals, call that v(t), via v(t)=inv(F)*u(t) where F is the "factor" matrix. You then generate the covariance matrix of v using the standard set of GARCH recursions, call that HV(t), as a function of its own lags and the lagged outer product of v(t). The covariance matrix of u(t) is then H=F*HV(t)*tr(F). The log likelihood is computed using %LOGDENSITY(H,u(t)).

While that's all quite doable, and not much more difficult than doing a standard MV-GARCH model by MAXIMIZE, it's not clear that's it's particularly useful. For instance, if you use a BEKK model for the GARCH, the parameters of the SVAR aren't identified; there's more than enough flexibility in unrestricted BEKK coefficient matrices to "undo" the SVAR model. This goes back to the original point, that both the SVAR and the GARCH model are trying to do somewhat the same thing.

[bekkdcc]

Dear Tom,

I am studying on the RATS Handbook for ARCH/GARCH and Volatility Models section 11. GARCH Models with Macroeconomic Data, An SVAR-GARCH-M model, in Table 11.1: Estimates of SVAR-GARCH-M Model, there is

G1(1) G1(2) G1(3) and
G2(1) G2(2) G2(3)

what are they, are they arch or garch coeffcients? How can I interpret them? and Also is there something to look for example as the sums (but which one) are near to 1 , etc....

[TomDoan]

Those are for univariate GARCH models on the structural residuals: (1) is the variance intercept, (2) is the coefficient on the lagged squared residual and (3) is the coefficient on the lagged variance. In this model, the first structural residual is the standard residual for oil price growth, but the second is a creation of the model.