VARSTABILITY.RPF

VARSTABILITY.RPF is an example of a Nyblom(1989) fluctuations test for a VAR. Note that a VAR has enough flexibility that it may be able to come up with a single set of estimates which can fit a set of data with a break sufficiently well that it passes a fluctuations test. (It may fit both subranges equally poorly).

Full Program

open data haversample.rat
calendar(q) 1959
data(format=rats) 1959:1 2006:4 dgnp fm2 gdph ih lr
*
set loggdp = 100.0*log(gdph)
set logm2 = 100.0*log(fm2)
set logp   = 100.0*log(dgnp)
set logi   = 100.0*log(ih)
set unemp = lr
*
system(model=usamodel)
variables loggdp unemp logi logp logm2
lags 1 to 4
det constant
end(system)
*
estimate(noprint,resids=resids) 1961:1 *
compute sigmainv=inv(%sigma)
*
dec vector s xt ut score %hstats
dec symm v vinv
*
* Compute sample information matrix
*
compute v=%zeros(%nregsystem,%nregsystem)
do time=%regstart(),%regend()
   compute ut=%xt(resids,time)
   compute xt=%eqnxvector(%modeleqn(usamodel,1),time)
   compute score=%kroneker(sigmainv*ut,xt)
   compute v=v+%outerxx(score)
end do time
*
compute v=%nobs*v
compute vinv=inv(v)
*
* Compute test statistics
*
compute s=%zeros(%nregsystem,1)
compute %hstats=%zeros(%nregsystem,1)
compute %hjoint=0.0
do time=%regstart(),%regend()
   compute ut=%xt(resids,time)
   compute xt=%eqnxvector(%modeleqn(usamodel,1),time)
   compute score=%kroneker(sigmainv*ut,xt)
   compute s=s+score
   ewise %hstats(i)=%hstats(i)+s(i)^2
   compute %hjoint=%hjoint+%qform(vinv,s)
end do time
ewise %hstats(i)=%hstats(i)/v(i,i)
*
report(action=define,title="Nyblom Test for VAR")
report(atrow=1,atcol=1) "Joint test" "" %hjoint %nyblomtest(%hjoint,%nregsystem)
*
compute ij=1
do i=1,%nvar
   do j=1,%eqnsize(%modeleqn(usamodel,1))
      report(row=new,atcol=1) %modellabel(usamodel,i) %eqnreglabels(%modeleqn(usamodel,1))(j) $
           %hstats(ij) %nyblomtest(%hstats(ij),1)
      compute ij=ij+1
   end do j
end do i
*
report(action=format,atcol=3,tocol=4,format="*.###")
report(action=show)

Output

Joint test 17.400807 0.509393

LOGGDP LOGGDP{1} 0.036875 0.946262

LOGGDP LOGGDP{2} 0.036875 0.946261

LOGGDP LOGGDP{3} 0.036886 0.946209

LOGGDP LOGGDP{4} 0.036894 0.946167

LOGGDP UNEMP{1} 0.035370 0.953455

LOGGDP UNEMP{2} 0.033872 0.960169

LOGGDP UNEMP{3} 0.034618 0.956886

LOGGDP UNEMP{4} 0.034505 0.957387

LOGGDP LOGI{1} 0.037753 0.941874

LOGGDP LOGI{2} 0.037748 0.941898

LOGGDP LOGI{3} 0.037593 0.942685

LOGGDP LOGI{4} 0.037750 0.941890

LOGGDP LOGP{1} 0.040375 0.928008

LOGGDP LOGP{2} 0.040458 0.927550

LOGGDP LOGP{3} 0.040542 0.927087

LOGGDP LOGP{4} 0.040594 0.926804

LOGGDP LOGM2{1} 0.039239 0.934150

LOGGDP LOGM2{2} 0.039284 0.933909

LOGGDP LOGM2{3} 0.039336 0.933633

LOGGDP LOGM2{4} 0.039396 0.933314

LOGGDP Constant 0.035430 0.953179

UNEMP LOGGDP{1} 0.024642 0.989980

UNEMP LOGGDP{2} 0.024666 0.989931

UNEMP LOGGDP{3} 0.024670 0.989922

UNEMP LOGGDP{4} 0.024684 0.989894

UNEMP UNEMP{1} 0.021566 0.995137

UNEMP UNEMP{2} 0.021149 0.995662

UNEMP UNEMP{3} 0.021779 0.994854

UNEMP UNEMP{4} 0.021953 0.994614

UNEMP LOGI{1} 0.024959 0.989313

UNEMP LOGI{2} 0.025162 0.988872

UNEMP LOGI{3} 0.025155 0.988888

UNEMP LOGI{4} 0.025298 0.988572

UNEMP LOGP{1} 0.025975 0.987005

UNEMP LOGP{2} 0.026021 0.986891

UNEMP LOGP{3} 0.026062 0.986794

UNEMP LOGP{4} 0.026147 0.986585

UNEMP LOGM2{1} 0.026150 0.986579

UNEMP LOGM2{2} 0.026166 0.986540

UNEMP LOGM2{3} 0.026140 0.986602

UNEMP LOGM2{4} 0.026083 0.986743

UNEMP Constant 0.023759 0.991700

LOGI LOGGDP{1} 0.054332 0.841732

LOGI LOGGDP{2} 0.054351 0.841607

LOGI LOGGDP{3} 0.054410 0.841222

LOGI LOGGDP{4} 0.054421 0.841148

LOGI UNEMP{1} 0.051600 0.859643

LOGI UNEMP{2} 0.047304 0.887080

LOGI UNEMP{3} 0.046886 0.889684

LOGI UNEMP{4} 0.047942 0.883078

LOGI LOGI{1} 0.056344 0.828416

LOGI LOGI{2} 0.056373 0.828225

LOGI LOGI{3} 0.056494 0.827418

LOGI LOGI{4} 0.056651 0.826379

LOGI LOGP{1} 0.060194 0.802810

LOGI LOGP{2} 0.060285 0.802203

LOGI LOGP{3} 0.060394 0.801476

LOGI LOGP{4} 0.060499 0.800778

LOGI LOGM2{1} 0.059303 0.808740

LOGI LOGM2{2} 0.059360 0.808357

LOGI LOGM2{3} 0.059460 0.807691

LOGI LOGM2{4} 0.059575 0.806930

LOGI Constant 0.051240 0.861981

LOGP LOGGDP{1} 0.102013 0.556576

LOGP LOGGDP{2} 0.102081 0.556244

LOGP LOGGDP{3} 0.102095 0.556180

LOGP LOGGDP{4} 0.102151 0.555906

LOGP UNEMP{1} 0.067265 0.756096

LOGP UNEMP{2} 0.067252 0.756180

LOGP UNEMP{3} 0.068414 0.748609

LOGP UNEMP{4} 0.073784 0.714250

LOGP LOGI{1} 0.106607 0.534863

LOGP LOGI{2} 0.106694 0.534461

LOGP LOGI{3} 0.107277 0.531783

LOGP LOGI{4} 0.107338 0.531508

LOGP LOGP{1} 0.105694 0.539093

LOGP LOGP{2} 0.105759 0.538789

LOGP LOGP{3} 0.105840 0.538413

LOGP LOGP{4} 0.105996 0.537690

LOGP LOGM2{1} 0.107117 0.532519

LOGP LOGM2{2} 0.107245 0.531932

LOGP LOGM2{3} 0.107353 0.531435

LOGP LOGM2{4} 0.107535 0.530605

LOGP Constant 0.098515 0.573831

LOGM2 LOGGDP{1} 0.043727 0.908862

LOGM2 LOGGDP{2} 0.043615 0.909526

LOGM2 LOGGDP{3} 0.043582 0.909718

LOGM2 LOGGDP{4} 0.043584 0.909708

LOGM2 UNEMP{1} 0.063642 0.779917

LOGM2 UNEMP{2} 0.062464 0.787718

LOGM2 UNEMP{3} 0.057701 0.819402

LOGM2 UNEMP{4} 0.057232 0.822519

LOGM2 LOGI{1} 0.042813 0.914223

LOGM2 LOGI{2} 0.042264 0.917395

LOGM2 LOGI{3} 0.041986 0.918985

LOGM2 LOGI{4} 0.041826 0.919897

LOGM2 LOGP{1} 0.045330 0.899251

LOGM2 LOGP{2} 0.045419 0.898708

LOGM2 LOGP{3} 0.045515 0.898125

LOGM2 LOGP{4} 0.045570 0.897787

LOGM2 LOGM2{1} 0.044737 0.902838

LOGM2 LOGM2{2} 0.044782 0.902564

LOGM2 LOGM2{3} 0.044857 0.902112

LOGM2 LOGM2{4} 0.044909 0.901799

LOGM2 Constant 0.043561 0.909842