*
* HAMILTON.RPF
* RATS Version 8, User's Guide, Example 11.3
*
* Hamilton Markov chain model for US GNP from page 697 of Hamilton,
* "Time Series Analysis"
*
cal(q) 1951:1
open data gnpdata.prn
data(format=prn,org=columns) 1951:1 1984:4
*
set g = 100*log(gnp/gnp{1})
graph(header="GNP growth")
# g
*
* Set up a mean-switching model with just the one variable and four lags.
*
@msvarsetup(lags=4,switch=m)
# g
compute gstart=1952:2,gend=1984:4
frml msvarf = log(%MSVARProb(t))
*
nonlin(parmset=msparms) p
nonlin(parmset=varparms) mu phi sigma
@msvarinitial gstart gend
*
* Estimate the model by maximum likelihood.
*
maximize(parmset=varparms+msparms,$
  start=(pstar=%MSVARInit()),$
  reject=%MSVARInitTransition()==0.0,$
  pmethod=simplex,piters=5,method=bfgs,iters=300) msvarf gstart gend
*
* Compute smoothed estimates of the states.
*
@msvarsmoothed gstart gend psmooth
set pcontract gstart gend = psmooth(t)(2)
*
* To create the shading marking the recessions, create a dummy series
* which is 1 when the recessq series is 1, and 0 otherwise. (recessq is
* 1 for NBER recessions and -1 for expansions).
*
set contract = recessq==1
*
spgraph(vfields=2)
graph(header="Quarterly Growth Rate of US GNP",shade=contract)
# g %regstart() %regend()
graph(style=polygon,header="Probability of Economy Being in Contraction",shade=contract)
# pcontract %regstart() %regend()
spgraph(done)