*
* Cointegration analysis of exchange rate data using
* ML procedure, pp 647-650
*
cal 1973 1 12
all 1989:10
open data exdata.rat
data(format=rats) / pc6it pzunew exritl
*
* Transform and normalize the data series
*
set italcpi = 100*log(pc6it)
set uscpi   = 100*log(pzunew)
set exrat   = -100*log(exritl)
*
set ditcpi = italcpi-italcpi{1}
set duscpi = uscpi-uscpi{1}
set dexrat = exrat-exrat{1}
*
cmom 1974:2 *
# duscpi dexrat ditcpi uscpi{1} exrat{1} italcpi{1} $
  ditcpi{1 to 11} duscpi{1 to 11} dexrat{1 to 11} constant
*
* "Sweeping" on a cross product matrix, in effect, regresses a
* set of variables on the pivots, leaving behind both regression
* coefficients and the cross product of residuals (or, in this
* case, because we've already scaled down by %nobs, the covariance
* matrix of residuals).
*
compute [rect] s=%cmom*(1.0/%nobs)
compute s=%sweeplist(s,%seq(7,%ncmom))
*
compute suu=%xsubmat(s,1,3,1,3)
compute svv=%xsubmat(s,4,6,4,6)
compute suv=%xsubmat(s,1,3,4,6)
*
compute sss=inv(svv)*tr(suv)*inv(suu)*suv
eigen sss eigval eigvec
disp
disp 'Unrestricted eigenvalues and T log(1-lambda)'
do i=1,3
  disp i eigval(i) %nobs*log(1-eigval(i))
end do i
*
* Pull the first eigenvector
*
compute a1=%xcol(eigvec,1)
*
* This normalizes a1 so that tr(a1)*Svv*a1=1
*
compute a1=a1*(1.0/sqrt(%qform(svv,a1)))
*
* And this normalizes a1 to have a unit coefficient in the first element
*
compute a1=a1*(1.0/a1(1))
disp 'Cointegrating vector'
disp a1
*
* Restriction from page 649
*
disp
disp "Test of restriction that exrate doesn't enter cointegrating relation"
compute d=||1.0,0.0|0.0,0.0|0.0,1.0||
compute svvr=tr(d)*svv*d
compute suvr=suv*d
compute sssr=inv(svvr)*tr(suvr)*inv(suu)*suvr
eigen sssr eigvalr eigvecr
disp
disp 'Restricted eigenvalues and T log(1-lambda)'
do i=1,2
   disp i eigvalr(i) %nobs*log(1-eigvalr(i))
end do i
*
* LR test of restriction given 1 cointegrating relation
*
compute lr=%nobs*log(1-eigvalr(1))-%nobs*log(1-eigval(1))
cdf chisqr lr 1
*
compute [vect] x1r=d*%xcol(eigvecr,1)
compute x1r=x1r*(1.0/x1r(1))
disp 'Restricted cointegrating vector'
disp x1r
*
*  Restriction from page 650
*
disp
disp "Test of restriction that cointegrating relation is PPP"
compute d=||1.0|-1.0|-1.0||
compute svvr=tr(d)*svv*d
compute suvr=suv*d
compute sssr=inv(svvr)*tr(suvr)*inv(suu)*suvr
eigen sssr eigvalr eigvecr
disp
disp 'Restricted eigenvalues and T log(1-lambda)'
do i=1,1
   disp i eigvalr(i) %nobs*log(1-eigvalr(i))
end do i
*
* LR test of restriction given 1 cointegrating relation
*
compute lr=%nobs*log(1-eigvalr(1))-%nobs*log(1-eigval(1))
cdf chisqr lr 2
*
compute x1r=d*%xcol(eigvecr,1)
compute x1r=x1r*(1.0/x1r(1))
disp 'Restricted cointegrating vector'
disp x1r