open greene18_2.gdt
# log of quarterly U.S. nominal GNP, 1950:1 to 1983:4
genr y = log(Y)
# and its first difference
genr dy = diff(y)
# log of real money supply (for ARMAX)
genr realm = log(M1/P)
# reserve 2 years for out-of-sample forecast
smpl ; 1981:4
# Estimate using ARIMA
arima 2 1 0 ; y 0 realm
# grab fitted values
genr fit1 = $yhat
# and forecast over full period
smpl --full
fcast fc1
# Return to sub-sample and do ARMA on first difference of y
smpl ; 1981:4
arma 2 0 ; dy 0 realm
genr fit2 = $yhat
smpl --full
fcast fc2
# generate series from fc1 which should agree with fc2: note the
# static and dynamic components
genr fcdiff = (t<=1982:1)? (fc1 - y(-1)) : (fc1 - fc1(-1))
# compare the forecasts
print y fc1 fc2 fcdiff --byobs
# generate series from fit1 which should agree with fit2
genr fitdiff = fit1 - y(-1)
# compare fitted values
print y fit1 fit2 fitdiff --byobs