State Space model specification

[Sheila]

Hi, could somebody please help me clarify what I am doing wrong. I keep getting “NA”s in the standard error and t-statistic columns for my constants (c(1)…c(3)) in the following SSPACE model.

Essentially, I am trying to estimate the following regression in order to obtain βt, the time-varying parameter, using the Kalman filter.


Measurement equation is given by: lnY_(j,t)-lnY_(i,t)= α_t+β_(i,t) (lnY_(j,t)-lnY_(l,t) )+ ε_t

and the state equation is given by: β_t=β_(t-1)+v_t


For simplicity, I generate ΔYj-i and ΔYj-l, to represent the dependent and explanatory variables, respectively. I then type the following command in the Eviews state space object:
@signal ΔYj-I,t = c(1) +sv1* ΔYj-l,t + [var= exp(c(2))]
@state sv1 = sv1(-1) + [var = exp(c(3))]
param c(1) .0 c(2) .0 c(3) .0

However, the output I get from this estimation looks something like this:

Sspace: SSPACE
Method: Maximum likelihood (Marquardt)
Date: 08/16/11 Time: 20:57
Sample: 2000M11 2010M10
Included observations: 120
Convergence achieved after 14 iterations
WARNING: Singular covariance - coefficients are not unique

Coefficient Std. Error z-Statistic Prob.

C(1) 2.015655 NA NA NA
C(2) -2318.518 NA NA NA
C(3) -6.174709 NA NA NA

Final State Root MSE z-Statistic Prob.

SV1 0.569629 0.045622 12.48571 0.0000

Log likelihood 130.7775 Akaike info criterion -2.129625
Parameters 3 Schwarz criterion -2.059937
Diffuse priors 1 Hannan-Quinn criter. -2.101324

[EViews Gareth]

The key is this part:
WARNING: Singular covariance - coefficients are not unique

Try different starting values, or changing the convergence criteria to something tighter.

[Sheila]

Hi Gareth,

Could you please clarify what you meant by "tighter convergence criteria"? Following your advice, I have tried various combinations of starting parameters and re-specifying the state equations however I have not had much luck still. With the following specification for instance, I get some results but the standard errors are quite large.

[@signal y_t = sv2 +sv1*x_t + [var = exp(c(1))]]
@state sv1 = c(4)*sv1(-1) + [var = exp(c(2))]
@state sv2 = sv2(-1) + [var = exp(c(3))]

param c(1) .0 c(2) .0 c(3) .0 c(4) .0

@mprior svec0
@vprior svar0

[EViews Gareth]

When you estimate the statespace model you can set the convergence criteria. Just set it to something smaller.