About output of DLM

[Jennylai]

Below are the output of DLM when I use it for kalman filtering technique:

DLM - Estimation by BFGS
Convergence in 16 Iterations. Final criterion was 0.0000003 <= 0.0000100
Quarterly Data From 1996:01 To 2008:01
Usable Observations 49
Rank of Observables 47
Log Likelihood -412.66666
Concentrated Variance 1643459.65313451

Variable Coeff Std Error T-Stat Signif
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1. V2 -2.860989177 1.564642475 -1.82853 0.06747067
2. V3 -9.391593494 8.763409183 -1.07168 0.28386260

May I ask what is the meaning of this "T-Stat"? As in MLE, we normally use LR, Wald, LM tests, this "T-stat" is really makes me confused.

Thank you very much for your kind attention and help.

[TomDoan]

Like most statistical software, RATS uses the phrase "t-statistic" to mean ratio between the coefficient and its (asymptotic) standard error. Where a t-statistic has an exact or at least approximate justification as being from an actual t (various univariate least squares procedures when there are no HAC covariance matrix corrections), the significance level is computed using the t-distribution. In all other cases (such as with DLM), the significance level is computed using the Normal

[Jennylai]

Thank you very much TomDoan!

I still got another question. Suppose my model is local linear trend model (y(t)=mu(t) + epsila(t),
mu(t) = mu(t-1)+beta(t-1)+kappa(t), beta(t)=beta(t-1)+gama(t), var(gama(t))=0.)

However, if the slope component beta in my state vectors has no error term in its equation, then my system would not be stabalizable. In this case, is it still viable to do this kind of normal test on estimates?

[TomDoan]

It would be more common to see var(kappa) being zero. var(gamma) means the trend rate is constant. Regardless, the t-stats still are asymptotically normal.