*
*  Illustration from section 2.8.1
*  Out-of-sample forecasting
*
open data nile.dat
calendar 1871
data(format=free,org=columns,skips=1) 1871:1 1970:1 nile
*
* To forecast out of sample, just run the filter beyond the range of the existing
* data.
*
dlm(y=nile,a=1.0,c=1.0,sx0=1.e+7,sv=15099.0,sw=1469.1,yhat=yhat,svhat=fhat) $
  1871:1 2000:1 xstates vstates
set a * 2000:1 = xstates(t)(1)
set p * 2000:1 = vstates(t)(1,1)
set lower * 2000:1 = a-%invnormal(.75)*sqrt(p)
set upper * 2000:1 = a+%invnormal(.75)*sqrt(p)
set f * 2000:1 = fhat(t)(1,1)
set y * 2000:1 = yhat(t)(1)
*
spgraph(footer="Figure 2.6. Nile data and output of forecasting",vfields=2,hfields=2)
graph(header="State forecast and 50% confidence intervals") 4
# a 1872:1 2000:1
# nile 1871:1 *
# upper 1872:1 2000:1 3
# lower 1872:1 2000:1 3
graph
# y 1872:1 2001:1
graph
# p 1872:1 2000:1
graph
# f 1872:1 2000:1
spgraph(done)