*
* SV.RPF
* RATS Version 8, User's Guide, Example 10.2
*
open data xrates.xls
data(format=xls,org=columns) 1 946 usxuk usxger usxjpn usxsui
*
* meanx2=mean of log chi-square,varx2=variance of log chi-square
*
compute meanx2=%digamma(0.5)-log(0.5)
compute varx2 =%trigamma(0.5)
*
* The "gamma" and "phi" variables are very highly correlated when phi is near 1,
* which makes estimation by general hill-climbing procedures somewhat tricky.
* Instead, we reparameterize this to use gammax=gamma(1-phi) in place of gamma.
*
set dlogp = log(usxuk{0}/usxuk{1})
diff(center) dlogp / demean
nonlin phi sw gammax
set ysq = log(demean**2)-meanx2
*
* Get initial guess values from ARMA(1,1) model
*
boxjenk(ar=1,ma=1,constant,noprint) ysq
*
* phi is taken directly as the AR(1) coefficient The variance sw is backed out by
* matching first order autocorrelations in the MA term. gamma is chosen to
* reproduce the mean of the ysq series
*
compute phi=%beta(2),sw=-phi*varx2*(1+%beta(3)**2)/%beta(3)-(1+phi**2)*varx2
compute sw=%if(sw<0,.1,sw)
compute gammax=%mean
*
* Estimate the unconstrained model
*
dlm(method=bfgs,sw=sw,sv=varx2,y=ysq,type=filter,c=1.0, $
   sx0=sw/(1-phi**2),x0=gammax,a=phi,z=gammax*(1-phi)) 2 * states
*
* Estimate the RW model
*
nonlin sw
dlm(method=bfgs,sw=sw,sv=varx2,y=ysq,type=filter,c=1.0, $
   exact,a=1.0,vhat=e,svhat=s) 2 * states