Statistics and Algorithms / GARCH Models / GARCH Models (Univariate) /

UV GARCH GARCH-M

ARCH-M models (Engle, Lilien, Robins(1987)) generalize the ARCH model by allowing a function of the variance to enter the mean model. The most common form of this uses the variance itself as a regressor. You can estimate an ARCH-M or GARCH-M model by using the special name %GARCHV among the regressors. This refers to the variance generated by the model. It behaves like a series, so you can include lags of it with the standard {...} notation. To add the current variance to an AR(1)-GARCH(1,1) model:

garch(p=1,q=1,regressors) / dlogdm

# constant dlogdm{1} %garchv

It’s important to note that if there is no “GARCH” there is no “M”—if the GARCH effect is weak, the GARCH variance is nearly constant so the “M” effect isn't identified.

Output

The built-in %GARCHV variable shows as GARCH-V in the output.

GARCH Model - Estimation by BFGS

Convergence in 22 Iterations. Final criterion was 0.0000000 <= 0.0000100

Dependent Variable DLOGDM

Usable Observations 1865

Log Likelihood -2058.8758

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. Constant -0.099950530 0.030934238 -3.23106 0.00123330

2. DLOGDM{1} -0.084561360 0.024189202 -3.49583 0.00047259

3. GARCH-V 0.160554894 0.056244288 2.85460 0.00430912

4. C 0.015099945 0.004519612 3.34098 0.00083483

5. A 0.108470775 0.016668724 6.50744 0.00000000

6. B 0.871554313 0.018356944 47.47818 0.00000000