cointegration with a state space model

[maragloria]

Hi there,

I am trying to estimate a state space model which involves a cointegration relationship among some known variables and the unknown factors.

Here is my code in Eviews 7:

@signal auqn = c(1)*cc1+ c(7)*cc2 + v1
@signal caqn = c(2)*cc1+ (c(8)+c(93)*dum)*cc2 + v2
@signal eurqn = c(3)*cc1+ c(9)*cc2 + v3
@signal gbqn = c(4)*cc1+ c(10)*cc2 + v4
@signal jpqn = c(5)*cc1+ c(11)*cc2 + v5
@signal nzqn = c(6)*cc1+ c(12)*cc2 + v6

@state cc1 = c(13)*cc1(-1) +c(14)*cc1lag(-1) + c(15)*pc1_r_diff(-1) + c(15)*pc1_debt_woaus(-1) + [var = exp(c(33))]
@state cc1lag = cc1(-1)
@state cc2 = c(17)*cc2(-1) + c(18)*cc2lag(-1) + c(19)*p_nonenr(-1) + c(20)*p_wtir(-1) + [var = exp(c(34))]
@state cc2lag = cc2(-1)

@state v1 = c(21)*v1(-1) + [var = exp(c(27))]
@state v2 = c(22)*v2(-1) + [var = exp(c(28))]
@state v3 = c(23)*v3(-1) + [var = exp(c(29))]
@state v4 = c(24)*v4(-1) + [var = exp(c(30))]
@state v5 = c(25)*v5(-1) + [var = exp(c(31))]
@state v6 = c(26)*v6(-1) + [var = exp(c(32))]

The variable "dum" in the signal section is a dummy variable containing 0s and 1s.
The variables pc1_r_diff, pc1_debt_woaus, p_nonenr, and p_wtir, in the first state section are the known variables I am cointegration with the unknow factors.

Once I run the code I get some estimates and the following warnings:

"Failure to improve Likelihood after 1 iteration"
"WARNING: Singular covariance - coefficients are not unique"

Here is the total result:

Sspace: SSPACE_FINAL
Method: Maximum likelihood (Marquardt)
Date: 06/29/10 Time: 13:20
Sample: 1981Q1 2007Q4
Included observations: 107
Failure to improve Likelihood after 1 iteration
WARNING: Singular covariance - coefficients are not unique

Coefficient Std. Error z-Statistic Prob.

C(1) -0.772732 NA NA NA
C(2) -0.498394 NA NA NA
C(3) -0.503291 NA NA NA
C(4) -0.471780 NA NA NA
C(5) -0.333279 NA NA NA
C(6) -0.694557 NA NA NA
C(7) 0.173199 NA NA NA
C(8) 0.006043 NA NA NA
C(9) -0.766201 NA NA NA
C(10) -0.467465 NA NA NA
C(11) -0.449248 NA NA NA
C(12) -0.031441 NA NA NA
C(13) 0.336333 NA NA NA
C(14) -9.42E-06 NA NA NA
C(15) 0.029872 NA NA NA
C(17) 0.208371 NA NA NA
C(18) -0.000982 NA NA NA
C(19) -0.153211 NA NA NA
C(20) 0.240025 NA NA NA
C(21) 0.210873 NA NA NA
C(22) 0.283526 NA NA NA
C(23) 0.206848 NA NA NA
C(24) 0.202781 NA NA NA
C(25) 0.205633 NA NA NA
C(26) 0.139830 NA NA NA
C(27) -1.286145 NA NA NA
C(28) -0.467473 NA NA NA
C(29) -150.8574 NA NA NA
C(30) -0.889399 NA NA NA
C(31) -0.505898 NA NA NA
C(32) -0.917505 NA NA NA
C(33) 0.000000 NA NA NA
C(34) 0.000000 NA NA NA
C(93) 0.083011 NA NA NA

Final State Root MSE z-Statistic Prob.

CC1 -0.561249 1.009914 -0.555740 0.5784
CC1LAG -1.587190 0.419711 -3.781627 0.0002
CC2 0.042599 1.001645 0.042529 0.9661
CC2LAG -0.267903 0.275694 -0.971743 0.3312
V1 0.031317 0.531498 0.058922 0.9530
V2 0.530758 0.794340 0.668175 0.5040
V3 1.20E-66 1.78E-33 6.75E-34 1.0000
V4 -0.135473 0.641170 -0.211290 0.8327
V5 -0.003325 0.776514 -0.004282 0.9966
V6 -0.038404 0.633308 -0.060641 0.9516

Log likelihood -807.2931 Akaike info criterion 15.72510
Parameters 34 Schwarz criterion 16.57441
Diffuse priors 10 Hannan-Quinn criter. 16.06940

Any suggestions?

Thanks for your help,

Mara