TVARYING.RPF

TVARYING.RPF is an example of time-varying parameters VAR. From the User's Guide, Sections 7.14.2,7.14.3.

Full Program

cal(q) 1959
open data haversample.rat
data(format=rats) 1959:1 2006:4 gdph fm1

log gdph
log fm1

compute kstart=1960:1,kend=2006:4

equation kalmeq gdph
# constant gdph{1 to 4} fm1{1 to 4}
declare vector b(9) bmean(9)
ewise bmean(i)=(i==2)
associate(perm) kalmeq b
*
linreg gdph
# constant gdph{1 to 4}
compute gseesq=.9*%seesq
linreg fm1
# constant fm1{1 to 4}
compute mseesq=.9*%seesq
*
* Set up the system. Use GSEESQ as the measurement equation variance
*
system kalmeq
kfset(constant,noscale,likelihood=likely) xxx
# gseesq
tvarying tvx
end(system)
*
* The hyperparameters (PIx) below are the following:
*   PI5 = Overall tightness. This corresponds to TIGHTNESS**2 on
*         SPECIFY.
*   PI2 = Relative tightness on other variables. This corresponds
*         to w**2 on the symmetric prior.
*   PI3 = Relative tightness on the constant. (No correspondence).
*   PI7 = Relative tightness on time variation.
*   PI8 = Shrinkage factor toward mean (between 0 and 1 , 1 = no shrinkage)
*
* This uses a HARMONIC decay with DECAY=.5
*
compute pi5 = .20**2
compute pi2 = .5**2
compute pi3 = 10000.
compute pi7 = 0.00000001
compute pi8 = 1.00
*
dim xxx(9,9) tvx(9,9)
*
compute likely=%const(0.0)
compute b=bmean
compute xxx=%const(0.0)
compute xxx(1,1)=pi5*pi3*gseesq
do i=1,4
compute decayfac=i**(-2*.5)
compute xxx(i+1,i+1)=pi5*decayfac
compute xxx(i+5,i+5)=pi5*pi2*decayfac*gseesq/mseesq
end do i
compute tvx=pi7*xxx
*
do time=kstart,kend
if time==kstart
     kalman(start=time)
else {
     compute b=pi8*b+(1-pi8)*bmean
     compute xxx=(pi8**2)*xxx
     kalman(print=(time==kend))
     }
end do time
*
* Compute the concentrated log likelihood
*
compute nobs=kend-kstart+1
compute loglikely=-.5*(likely(1,1)+nobs*log(likely(2,1)/nobs))

compute pi5 = .20**2 , pi2 = .5**2 , pi3 = 10000.
compute pi7 = 0.00000001 , pi8 = 1.00
nonlin pi8 pi7
dec real loglikely
dim xxx(9,9) tvx(9,9)
find(method=genetic,iterations=200) maximum loglikely {
   if pi7<0.or.pi8>1.00 {
      compute loglikely=%na
      next
   }
   compute likely=%const(0.0)
   compute b=bmean
   compute xxx=%const(0.0)
   compute xxx(1,1)=pi5*pi3*gseesq
   do i=1,4
     compute decayfac=i**(-2*.5)
     compute xxx(i+1,i+1)=pi5*decayfac
     compute xxx(i+5,i+5)=pi5*pi2*decayfac*gseesq/mseesq
   end do i
   compute tvx=pi7*xxx
*
   do time=kstart,kend
      if time==kstart
       kalman(start=time)
      else {
        compute b=pi8*b+(1-pi8)*bmean
        compute xxx=(pi8**2)*xxx
        kalman
    }
   end do time
   compute nobs=kend-kstart+1
   compute loglikely=-.5*(likely(1,1)+nobs*log(likely(2,1)/nobs))
}
end find

Output

Linear Regression - Estimation by Least Squares

Dependent Variable GDPH

Quarterly Data From 1960:01 To 2006:04

Usable Observations 188

Degrees of Freedom 183

Centered R^2 0.9996540

R-Bar^2 0.9996464

Uncentered R^2 0.9999991

Mean of Dependent Variable 8.6324850619

Std Error of Dependent Variable 0.4316368147

Standard Error of Estimate 0.0081162154

Sum of Squared Residuals 0.0120547504

Regression F(4,183) 132178.6002

Significance Level of F 0.0000000

Log Likelihood 640.7850

Durbin-Watson Statistic 1.9626

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. Constant 0.020392668 0.012056163 1.69147 0.09244878

2. GDPH{1} 1.217407118 0.073758692 16.50527 0.00000000

3. GDPH{2} -0.058554015 0.115526790 -0.50684 0.61287472

4. GDPH{3} -0.186799332 0.113578117 -1.64468 0.10175309

5. GDPH{4} 0.026197898 0.072293464 0.36238 0.71748424

Linear Regression - Estimation by Least Squares

Dependent Variable FM1

Quarterly Data From 1960:01 To 2006:04

Usable Observations 188

Degrees of Freedom 183

Centered R^2 0.9998897

R-Bar^2 0.9998873

Uncentered R^2 0.9999983

Mean of Dependent Variable 6.1687053805

Std Error of Dependent Variable 0.7805932208

Standard Error of Estimate 0.0082873900

Sum of Squared Residuals 0.0125685923

Regression F(4,183) 414713.0563

Significance Level of F 0.0000000

Log Likelihood 636.8612

Durbin-Watson Statistic 2.0063

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. Constant 0.008971455 0.004931246 1.81931 0.07049880

2. FM1{1} 1.532889693 0.072875519 21.03436 0.00000000

3. FM1{2} -0.376453959 0.133875853 -2.81196 0.00546115

4. FM1{3} -0.111167371 0.134237861 -0.82814 0.40867149

5. FM1{4} -0.046206319 0.073345862 -0.62998 0.52949443

VAR/System - Estimation by Kalman Filter

Quarterly Data From 1960:01 To 2006:04

Usable Observations 188

Dependent Variable GDPH

Mean of Dependent Variable 8.6324850619

Std Error of Dependent Variable 0.4316368147

Standard Error of Estimate 0.0080077164

Sum of Squared Residuals 0.0120552222

Durbin-Watson Statistic 1.8412

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. Constant 0.086552765 0.044251977 1.95591 0.05047607

2. GDPH{1} 1.161107016 0.059304239 19.57882 0.00000000

3. GDPH{2} -0.039702753 0.080713454 -0.49190 0.62279175

4. GDPH{3} -0.109263931 0.071434525 -1.52957 0.12612381

5. GDPH{4} -0.026476913 0.050557162 -0.52370 0.60048547

6. FM1{1} 0.059896869 0.039870927 1.50227 0.13302758

7. FM1{2} -0.021374042 0.053186735 -0.40187 0.68778124

8. FM1{3} -0.048988569 0.043814137 -1.11810 0.26352445

9. FM1{4} 0.017437230 0.031481233 0.55389 0.57965218

FIND Optimization - Estimation by Genetic

Convergence in 34 Iterations. Final criterion was 0.0000063 <= 0.0000100

Function Value 891.4792

Variable Coeff

**********************************************

1. PI8 0.99503

2. PI7 1.79506e-008