GJR-GARCH Model
Another asymmetric GARCH process is the GJR-GARCH model of Glosten, Jagannathan and Runkle (1993). They propose modeling , where vt is i.i.d. with zero mean and unit variance, and
where It-1=1 if and It-1=0 if ut-1<0.
You can use the following code to estimate a GJR-GARCH(1,1) model.
/* Estimate GJR-GARCH Model */
proc model data = gjrgarch ;
parms arch0 .1 arch1 .2 garch1 .75 phi .1;
/* mean model */
y = intercept ;
/* variance model */
if zlag(resid.y) > 0 then
h.y = arch0 + arch1*xlag(resid.y**2,mse.y) + garch1*xlag(h.y,mse.y) ;
else
h.y = arch0 + arch1*xlag(resid.y**2,mse.y) + garch1*xlag(h.y,mse.y) +
phi*xlag(resid.y**2,mse.y) ;
/* fit the model */
fit y / method = marquardt fiml ;
run ; quit;