State Space model with TVC, recovering TVC and residuals

[bmpc]

I'm estimating a TVC by maximum likelihood. I use the state conditions to get time varying coefficients that will then be decomposed into biased and unbiased components. The idea is that if sv2 is the total coefficient sv2-c(2)-c(3)-error term will be the unbiased estimate of the coefficients.

I can get the time varying series for sv2, but i can't get the residuals of the equation nor the time varying coefficients series of the coefficients of the state equation. My interest is precisely on the components of the state, not the components of the signal equation.

Can anybody help? Thanks

The code is as follows:

@signal A= sv1+sv2*B
@state sv1= c(1)+c(2)*C+c(3)*D+c(5)*E+[var=exp(negative number)]
@state sv2 = c(7)+c(8)*B+c(9)*F+c(10)*G+c(12)*H+[var=exp(negative number)]

[startz]

Something like

Code: Select all

series residual = sv1 - ( c(1)+c(2)*C+c(3)*D+c(5)*E)

[bmpc]

That seems to work, do you think it uses the time varying c(?) rather than the summary statistic appearing on estimation output? Any idea about a way to generate series for c(?) coefficients? Thanks!

[startz]

The c() coefficients aren't time varying. To have time-varying coefficients you need to represent the coefficients as states.

[bmpc]

But when i see the gradients of the ML function they are time varying. I'm following a paper that states "the total value of this TVC [like my sv2] and the bias free component are represented below, with the bias free effect given by subtracting the error term and the effect from C and D" i interpreted this effect being the time varying C(?) of that variable. Am i wrong?

[startz]

But when i see the gradients of the ML function they are time varying. I'm following a paper that states "the total value of this TVC [like my sv2] and the bias free component are represented below, with the bias free effect given by subtracting the error term and the effect from C and D" i interpreted this effect being the time varying C(?) of that variable. Am i wrong?

I'm afraid you're wrong. C(?) is just a single number. You can click on c in the workfile and see what the number is.

[bmpc]

You were completely right. And of a big help. I have one additional question. Often when I'm changing the specification of my State space model eviews goes crazy and gives completely strange coefficients in the estimation. My coefficients usually range from -5 to 5, and sometimes I get a coefficient of 25000, or a similar unreasonable number. The strangest thing is that even if I change the coefficient the value remains, while the estimation output stops at one iteration. Generally I have to create a SSpace from the scratch to be able to get reasonable estimations.

Is there any reason for this? This has happened in different versions of eviews, in different computers, and as I'm trying several combinations of variables to address one problem that is keeping me to end my work.

Thanks in advance

[startz]

State-space models sometimes have very nonlinear likelihood functions. That means that the results depend on starting values and the algorithm used.

There often isn't much to do but try different starting values and note which one seems to have ended up in the globally best likelihood value.

[bmpc]

But the thing is that i'm not specifying the initial values, as I'm dealing with time series variables I have no ideia about initial values of coefficients, specially considering I would have to set them for the state equations, for which I can't formulate an OLS counterpart.

Do you think I should try specifying initial values? do you think i could get better results? I'm basically estimating 3 sspaces to get 3 coefficients of interest, with each ss having 3 state equations with several variables.

[startz]

EViews uses whatever coefficients are in the C vector. So you should check C before running.