Understanding Garch Output

[kvansek]

I used data to try and estimate a GARCH-M model using the garch command as below

Code: Select all

garch(regressors) 1 500 y 
#x

and receive this as output:

GARCH Model - Estimation by BFGS
Convergence in 28 Iterations. Final criterion was 0.0000000 <= 0.0000100
Usable Observations 500
Log Likelihood -1137.12587183

Variable Coeff Std Error T-Stat Signif
*******************************************************************************
1. X 4.0227068796 0.0362796367 110.88057 0.00000000
2. C 1.8448273707 0.4271727158 4.31869 0.00001570
3. A 0.2933550919 0.0708330940 4.14150 0.00003450
4. B 0.4118054877 0.0958896505 4.29458 0.00001750

My data was generated from a y equation of the form : y = constant + 3*x+0.8*sqrt(h)+e (error)
Am I right in saying that X refers to the estimate of X, C to the constant, A to H and B to E?

[TomDoan]

The C, A and B are for the GARCH model of the variance. The X is for the X in the mean model. You need to include the CONSTANT as well with your regressors. With the built-in GARCH, you can put the GARCH variance into the mean model by using %GARCHV, that is,

Code: Select all

garch(regressors) 1 500 y 
# constant x %garchv

With RATS 8.1, you can do the transformation to the square root as part of the GARCH instruction using the HADJUST option:

Code: Select all

set sqrth = 0.0
garch(hseries=he,hadjust=(sqrth=sqrt(he(t))),regressors) 1 500 y
# constant x sqrth

For an similar example for earlier versions of RATS, see the example tsayp663.rpf from the Tsay textbook replications.