*
* GARCH example from pp 116-123
*
calendar(m) 1926
open data ch03_sp500_m(26-91).dat
data(format=free,org=columns) 1926:1 1991:12 sp500
*
set retsq = sp500**2
@bjident(number=30,nozero,max=.15) sp500
@bjident(number=30,nozero,max=.35) retsq
*
boxjenk(constant,ma=||1,3||) sp500
boxjenk(constant,ar=3) sp500
*
garch(regressors,p=1,q=1) / sp500
# constant sp500{1 2 3}
garch(regressors,p=1,q=1) / sp500
# constant %mvgavge{1 3}
garch(p=1,q=1,hseries=ht,resids=at) / sp500
set ahat = at/sqrt(ht)
graph(header="Estimated Volatility")
# ht
graph(header="Standardized Residuals")
# ahat
*
* Forecast 120 periods beyond the end of the data
*
set uu = at**2
compute vc=%beta(2),vb=%beta(4),va=%beta(3)
frml hfrml  ht = vc+vb*ht{1}+vc*uu{1}
frml uufrml uu = ht
group garchmod hfrml>>ht uufrml>>uu
forecast(model=garchmod,from=1992:1,steps=120)
*
garch(p=1,q=1,hseries=ht,resids=at,dist=t,shape=5) / sp500
set ahat = at/sqrt(ht)
set ahatsq = ahat**2
@RegCorrs(number=30) ahat
@RegCorrs(number=30) ahatsq
garch(p=1,q=1,hseries=ht,resids=at,dist=t) / sp500
garch(regressors,p=1,q=1) / sp500
# constant %mvgavge{1 2}
*
* This is the GARCH-M from page 123
*
garch(regressors,p=1,q=1,condition) / sp500
# constant %garchv