estimation result from Kalman Filter

[kaner]

Hello all,
I am trying to estimate the time varying parameter using state space model in eviews6.
the model is like this (in general form)

signal equation
yt = xtβt + ztAt + et et ∼ N(0, R)

state equation
βt = βt−1 + vt vt ∼ N(0, Q)
At = At−1 + wt wt ∼ N(0, H)

my questions are

1.) After getting the result of β which is time varying parameter, is it possible that β is stationary?

2.) I accidentally use the unit root test on it and it is stationary. I wonder if my β is incorrect because, according to the state equation, I specified it as random walk.

3.) (this question is not specific for this result but for general case) Can I say that the state space estimation in eviews (i mean by click "estimate" in "sspace") is already applied Kalman filter?

Thank you very much in advance for your help.

kaner

[trubador]

Coefficients do not have to be stationary. Random walk is the most flexible and general specification for the stochastic law-of-motion as it can generate any type of dynamics including time-invariant/fixed parameters. If your estimation of the parameter turns out to be stationary, then you can try AR(1) specification for that parameter. This will also allow you to compute its long-run value.

And yes, Kalman filter is built-in in the sspace object.

[kaner]

Thank you very much, trubador :D

[kaner]

Oh I have more questions!!

Does anyone know that after estimating time varying parameter model and get the smoothed state varibales, do we need to report any goodness of fit of the model?
and if yes, how can we get something like R-squaerd or others?
Or only the log-likelihood and AIC and SIC providing with the "stats" window are enough?

Thank you very much in advance for your help!!