*
* Example 4.4 from pp 164
* STAR-ARCH model
*
open data ch04_3m_m(46-97).txt
calendar(m) 1946:2
data(format=free,org=columns) 1946:2 1997:12 date returns
*
* Estimate ARCH(2)
*
garch(q=2) / returns
*
* STAR-ARCH model
*
nonlin(parm=meanparms) b0
nonlin(parm=garchparms) c a1 a2
nonlin(parm=starparms) sc sa1
linreg returns / u
# constant
set uu = %seesq
set h  = %seesq
compute b0=%beta(1),c=%seesq,a1=a2=.01,sc=0.0,sa1=0.0
*
frml resid = returns-b0
frml hf    = (c+a1*uu{1}+a2*uu{2})+(sc+sa1*uu{1})/(1+exp(-1000*u{1}))
frml logl  = (u=resid),(uu=u**2),(h=hf),%logdensity(h,u)
maximize(parmset=meanparms+garchparms+starparms) logl