options crt;
name archf 'Forecasting h(t) from GARCH model' ;
?
?  To forecast ARCH variances into the future, you can use a dynamic 
?  GENR. This is an example using simulated data.
?
?  TSP 4.2B (July 1994)
?  Author: Clint Cummins
?
smpl 1,100;
RANDOM(seed=4211947) X E;  ? draw some data from a true GARCH(1,1) model
h = 1;

smpl 2,100;
h = 1 + .3*e(-1)*e(-1)*h(-1) + .5*h(-1);   ? Dynamic GENR for h(t).

smpl 1,100;
y = 1 + 2*x + e*sqrt(h);
ARCH Y C X;        ? default GARCH(1,1) -- 6 coefs are C X A0 A1 B1 H(0)
unmake @COEF g1 g2 a0 a1 b1 h0;
E = @RES/sqrt(@HT);           ? standardized residuals
H = @HT;                      ? std dev. of residuals

smpl 101,110;  E = 1;         ? so that square of E is "unit" normal
H = A0 + A1*E(-1)*E(-1)*H(-1) + B1*H(-1);  ? Dynamic forecast of h(t).

smpl 90,110; print h;         ? Display last 10 actual variances and
                              ? the 10 forecast values.