generalized state-space models?

[Novi]

Hi!
I am new at state-space models estimation in Eviews so forgive me if this question is silly :)
In Eviews 6 user manual II, on page 384 I read:

"In the discussion that follows, we will generalize the specification given in (35.1)—(35.3) by allowing the system matrices and vectors [c,d, Z,...] to depend upon observable explanatory variables and unobservable parameters "

However, I am studying Harvey (1981), which is also quoted as a refecence by this chapter, and there it explicitly says that in the state space representation the system matrices and vectors [c,d, Z,...] must be fixed, and they cannot depend on anything.
Hence, what is the link I am missing? Is there something I should read about how to generalize the specification? how is this practically implemented in the Eviews routine?

Any help will be greatly appreciated! thx :D

[EViews Glenn]

If I'm understanding your question....

I'm not certain which statement in Harvey you are referring to, so it's a little difficult for me to respond directly. The standard extension has the system matrices fixed, conditional on a set of parameter values (and data). You can then treat these parameters as part of the likelihood estimation. Note that estimates of variances of processes from the Kalman filter do not account for these estimated unknowns. Hamilton has an article on doing simulation to obtain alternative variance measures.

[Novi]

Dear Glenn
Thx for the quick reply...Again I might be the one that is not understanding something, so I'll try to clarify more my question, and please excuse me if I say something naive :D
I am referring to the standard state space framework (Harvey, 1981, page 101 for example) where both in the measurement and in the signal equation, system matrices are fixed, i.e. they only contain known parameters.
I'll elaborate a bit what I don't understand with an example:
Take page 390 of the views 6 users guide II, the following specification is given:
log(passenger) = c(1) + c(3)*x + sv1 + c(4)*sv2

However, as I understood it the signal equation should only contain state variables multiplied for their respective parameters [here sv1 + c(4)*sv2], and not exogenous variables whose parameter needs to be estimated [here c(3)*x], Where am I going wrong?
What you say is that there is a standard extension where system matrices are still fixed but they are conditional on a set of parameter values and data, which then you have inside the likelihood function...could you give me a reference for this standard extension? sorry I don't know it :( also if you can find the exact reference for that Hamilton's article on obtaining alternative variance measures in this framework, I would really appreciate it!

Many many thanks

[startz]

Dear Glenn
Thx for the quick reply...Again I might be the one that is not understanding something, so I'll try to clarify more my question, and please excuse me if I say something naive :D
I am referring to the standard state space framework (Harvey, 1981, page 101 for example) where both in the measurement and in the signal equation, system matrices are fixed, i.e. they only contain known parameters.
I'll elaborate a bit what I don't understand with an example:
Take page 390 of the views 6 users guide II, the following specification is given:
log(passenger) = c(1) + c(3)*x + sv1 + c(4)*sv2

However, as I understood it the signal equation should only contain state variables multiplied for their respective parameters [here sv1 + c(4)*sv2], and not exogenous variables whose parameter needs to be estimated [here c(3)*x], Where am I going wrong?
What you say is that there is a standard extension where system matrices are still fixed but they are conditional on a set of parameter values and data, which then you have inside the likelihood function...could you give me a reference for this standard extension? sorry I don't know it :( also if you can find the exact reference for that Hamilton's article on obtaining alternative variance measures in this framework, I would really appreciate it!

Many many thanks

In case this helps:

unknown parameters:
The Kalman filter is used to evaluate the likelihood function given a set of parameters, say a value for c(4). What EViews does is try out different values for c(4), uses the Kalman filter to compute the likelihood for each value, and then reports back the value that maximized the likelihood.

exogenous variables:
Think of the signal equation as explaining log(passenger) - (c(1) + c(3)*x). Note that the intercept is just as much an exogenous variable as is x.

[EViews Glenn]

Looking at your Harvey reference I am certain that he is speaking about fixed stochastically relative to the likelihood. There is nothing in the discussion that indicates that the system matrices must be fixed numbers. Indeed, many ARMA representations have system matrices that depend on parameters...

As to references:

[1] Harvey (1989). Forecasting, structural time series models and the Kalman Filter. Cambridge: Cambridge University Press.

(p. 103.) "The system matrices, Z_t, H_t, T_t, R_t and Q_t may depend on a set of unknown parameters, and one of the main statistical tasks will often be estimation of these parameters."

[2] Hamilton (1986). "A Standard Error for the Estimated State Vector of a State-Space Model," Journal of Econometrics, Dec. 1986

[Novi]

Dear Glenn and dear Starz,
Thank u both very much for your replies! :D
Now I understand the point you are stressing: indeed to run the Kalman filter routine parameters HAVE TO BE KNOWN, and in order to have an estimate of their values eviews allows us to do a ML estimation on the system in state space form (hence the procedure 'make kalman filter', after the state-space system is estimated!). I guess I got confused between the filtering routine and the ml estimation, even if the two are closely related!

Can I ask an additional question to Glenn? :) I see that the eviews specification for the state-space object requires that state equations are linear in states right? then will I be allowed to express some nonlinear model (like smooth transition models/markov switching models) in state-space form in eviews?

Many many thanks again

[EViews Glenn]

Not easily. Depending on what smooth transition model you have in mind, you may be able to do it with non-linear least squares. The Markov Switching model is more difficult due to the probability restrictions. You should search the forum for Trubador's code which estimates the Hamilton form of the switching model for 2 states...(just search for Markov Switching and you'll see a bunch of stuff).

[Novi]

Thx! :)