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open data lgdp.txt
calendar(q) 1947
data(format=free,org=columns) 1947:01 1998:02 lgdp
*
* Everything is run on 100*log data
*
set lgdp = 100.0*lgdp
*
@NBERCycles(down=recession)
*
* UC-0 decomposition with AR(2) cycle, fixed trend rate.
*
nonlin mu sn ph1 ph2 se
*
dec frml[rect] af
dec frml[vect] zf
dec frml[symm] swf
*
frml af = ||1.0,0.0,0.0|$
            0.0,ph1,ph2|$
            0.0,1.0,0.0||
frml zf = ||mu,0.0,0.0||
frml swf = %diag(||sn^2,se^2||)
*
compute [vect] c=||1.0,1.0,0.0||
compute [rect] f=%identity(2)~~%zeros(1,2)
*
* Get initial guess values
*
filter(type=hp) lgdp / gdp_hp
set gap_hp = lgdp - gdp_hp
linreg gap_hp
# gap_hp{1 2}
compute ph1=%beta(1),ph2=%beta(2),se=sqrt(%seesq)
set trend = t
linreg gdp_hp
# constant trend
compute mu=%beta(2)
compute sn=sqrt(.1*%seesq)
*
* In order to be comparable with the BN decomposition (which is a
* "filtered" calculation), this uses filtered rather than smoothed
* estimates of the components.
*
dlm(presample=ergodic,a=af,z=zf,sw=swf,c=c,f=f,y=lgdp,method=bfgs,type=filter) / states0
*
set cycle0 = states0(t)(2)
set trend0 = states0(t)(1)
*
graph(footer="Figure 1 UC-0 Cycle, US Real GDP. Percent Deviation from Trend",$
  shaded=recession)
# cycle0

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frml zf = ||mu,0.0,0.0||
frml swf = ||sn^2|rhone*sn*se,se^2||
dlm(presample=ergodic,a=af,z=zf,sw=swf,c=c,f=f,y=lgdp,method=bfgs,type=filter) / statesur
set cycleur = statesur(t)(2)
set trendur = statesur(t)(1)
*
graph(footer="Figure 3 UC-UR Cycle, US Real GDP",$
  shaded=recession)
# cyclebn

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ompute bench = %logl
set ll  = 0.0
set rho  = 0.0

compute xrho = -0.95
* From -0.95 to 0.95
do i = 1, 39, 1


   nonlin mu sn ph1 ph2 se rhone=xrho

   dlm(presample=ergodic,a=af,z=zf,sw=swf,c=c,f=f,y=lgdp,method=bfgs,type=filter) / statesur
   compute ll(j) = %logl
   compute rho(j) = xrho
   compute xrho = xrho+0.05

end do
set ratio = 0.0
do  j = 1, 39, 1
      compute ratio(j) = -2*(ll(j)-bench)
end do
set chi2 1 39 = 3.8415

scatter(style=lines,header="Likelihood Ratio Statistics For Testing RhoNE = RhoNE,0",$
        hlabel="RhoNE,0",$
        vlabel="LR Statistics") 2
   # rho ratio 1 39
   # rho chi2 1 39 3

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@gridseries(from=-.99,to=.99,size=.01,pts=ngrid) rhos
set lrstat 1 ngrid = 0.0
nonlin mu sn ph1 ph2 se
*
* Reset to the full optimum coefficients
*
compute %parmspoke(fullset,baseparms)
do i=1,ngrid
   compute rhone=rhos(i)
   if i<>1
      dlm(presample=ergodic,a=af,z=zf,sw=swf,c=c,f=f,y=lgdp,method=bfgs,hessian=%xx,type=filter)
   else
      dlm(presample=ergodic,a=af,z=zf,sw=swf,c=c,f=f,y=lgdp,method=bfgs,type=filter)
   compute lrstat(i)=-2.0*(%logl-baselogl)
end do i
scatter(style=line,footer="Figure 4 Likelihood Ratio Tests for Testing Value of Rho")
# rhos lrstat