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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

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

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

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

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