Wondering about state space model

[startz]

I have a state space model which is really just two lags of a variable. The results look nothing like a least squares regression. have I misspecified something?

My model is

Code: Select all

@state t = c(2) + c(3)*t(-1) + c(4)*tlag(-1) + [var=exp(c(5))] @state tlag = t(-1) @signal div=t

The results are
Sspace: AGSSMODEL
Method: Maximum likelihood (Marquardt)
Date: 10/02/09 Time: 11:54
Sample: 1926Q1 2007Q1
Included observations: 325
Convergence achieved after 1 iteration

Coefficient Std. Error z-Statistic Prob.

C(2) -0.000759 1.18E-10 -6445524. 0.0000
C(3) 0.999749 8.34E-15 1.20E+14 0.0000
C(4) 0.000251 9.71E-12 25830990 0.0000
C(5) -23.04932 1.45E-09 -1.59E+10 0.0000

Final State Root MSE z-Statistic Prob.

T 0.237124 9.88E-06 23992.28 0.0000
TLAG 0.237864 0.000000 NA 0.0000

Log likelihood -7.19E+11 Akaike info criterion 4.43E+09
Parameters 4 Schwarz criterion 4.43E+09
Diffuse priors 0 Hannan-Quinn criter. 4.43E+09


In contrast, an ols regression gives
Dependent Variable: DIV
Method: Least Squares
Date: 10/02/09 Time: 11:41
Sample (adjusted): 1926Q3 2007Q1
Included observations: 323 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

C 0.017051 0.005720 2.980952 0.0031
DIV(-1) 0.523837 0.050826 10.30655 0.0000
DIV(-2) 0.397678 0.049719 7.998471 0.0000

R-squared 0.838684 Mean dependent var 0.231201
Adjusted R-squared 0.837676 S.D. dependent var 0.101244
S.E. of regression 0.040791 Akaike info criterion -3.551489
Sum squared resid 0.532438 Schwarz criterion -3.516402
Log likelihood 576.5654 Hannan-Quinn criter. -3.537482
F-statistic 831.8423 Durbin-Watson stat 2.142097
Prob(F-statistic) 0.000000

[EViews Glenn]

I may be missing something here, but I'm not certain what you expect to see.

You've specified the signal equation as a function of a single unobserved AR(2) state which, if I'm not mistaken, is very different than modeling it as a function of the lags of the observed dependent variable (in the same way that an AR isn't the same as the unrestricted autoregression).

[startz]

But in this case the signal is exactly the state. So the whole thing should be observed.

Also, isn't
ls y y(-1) y(-2)

exactly an AR(2)?

[EViews Glenn]

Actually, you're right. Since there are no explanatory variables they should be the same.

In any event, your coefficients clearly haven't converged from the starting values...What do the gradients look like? What happens at different values?

Or you can post the workfile...