*
* Chapter 8 - Norway data
*
open data norwayfinland.txt
calendar(a) 1970
data(format=free,org=columns,skips=1) 1970:01 2003:01 year norway finland
*
set lognorway = log(norway)
*
@LocalDLMInit(irreg=sigsqeps) lognorway
nonlin sigsqeps sigsqxi
compute sigsqxi=sigsqeps*.01
*
* For comparison, we need both filtered and smoothed estimates
*
dlm(a=1.0,c=1.0,sv=sigsqeps,sw=sigsqxi,exact,y=lognorway,$
  method=bfgs,vhat=vhat,svhat=svhat) / fstates
dlm(a=1.0,c=1.0,sv=sigsqeps,sw=sigsqxi,exact,y=lognorway,$
  type=smooth) / sstates
*
* The graph doesn't quite match because of a different definition of
* "filtered" state. For the RATS DLM instruction, the filtered state is
* the expectation of X(t) given information through t. In the text, the
* filtered state is the expectation of X(t) given information through
* t-1. "Smoothed" means the same regardless.
*
set filtered = %scalar(fstates)
set smoothed = %scalar(sstates)
graph(footer="Smoothed and filtered state of the local level model",$
  key=upright,klabels=||"smoothed level","filtered level"||) 2
# smoothed
# filtered
*
set perror = %scalar(vhat)
set pevar  = %scalar(svhat)
*
* The prediction error and prediction error variance really only make
* sense for entries 2 and above (or, in general, beyond the number of
* unit roots in the state-space model).
*
spgraph(vfields=2,samesize,$
 footer="Figure 8.7 One-step ahead prediction errors and their variances")
graph(key=upleft,klabels=||"prediction errors"||)
# perror 2 *
graph(key=upright,klabels=||"prediction error variance"||)
# pevar  2 *
spgraph(done)