TVP estimation

[Charweise]

Can anyone help me figure out what I'm doing wrong? I must be fundamentally misunderstanding something about Sspace estimation. I'm trying to estimate an augmented Taylor rule equation with time-varying parameters. I set up the model like so:

f = sv1 + sv2*f(-1) + sv3*p + sv4*y + sv5*s + [VAR=EXP(C(1))]
@STATE SV1 = SV1(-1) + [VAR=EXP(C(2))]
@STATE SV2 = SV2(-1) + [VAR=EXP(C(3))]
@STATE SV3 = SV3(-1) + [VAR=EXP(C(4))]
@STATE SV4 = SV4(-1) + [VAR=EXP(C(5))]
@STATE SV5 = SV5(-1) + [VAR=EXP(C(6))]

and I keep getting the error "WARNING: Singular covariance - coefficients are not unique." I have tried simpler versions of the model with the same result.

[EViews Glenn]

Do you really want your TVP to evolve as random walks?

[Charweise]

Yes I do. Why do you ask?

[EViews Glenn]

Just checking. Specifying random walk coefficients can lead to the behavior you see if the data are stationary. Beyond that, you're going to have to post your workfile as the model you specified may work for some data but not for others.

[Charweise]

The data is in fact stationary, but I think the assumption of random walk parameters is pretty standard. I've never heard of others having a problem with stationary data. Is there a problem with having all the error terms have unrestricted variances? Here's the file.

[EViews Glenn]

For your data, likelihood maximization wants several of the state variances to go to zero which is why you are getting singularity. To get a better handle on what is going on, I experimented with some simple specifications.

A simple random coefficient spec "works" (as in estimates):

Code: Select all

@signal f = sv1 + sv2*f(-1) + sv3*p + sv4*y + sv5*s + [var=exp(c(6))] @state sv1 = c(1) + [var = 0] @state sv2 = c(2) + [var = exp(c(7))] @state sv3 = c(3) + [var = exp(c(8))] @state sv4 = c(4) + [var = exp(c(9))] @state sv5 = c(5) + [var = exp(c(10))]

when I start from the least squares coefficients, but even here there is evidence that variances are near zero (note that I leave out a variance for the SV1 state as the random constant variance is not identified in this specification).

I can get a model with a random walk coefficients on F(-1) and S, and fixed coefficients for the other variables, but when I add random coefficients to any of the other variables it drives variances to zero.

To me, that suggests that there are very few random coefficients in these data, but that's just based on my brief playing with the data. There are lots of combinations of specifications that one can do but my sense is that the data don't support full random coefficient specifications for all of the variables. Others who work with these types of models on a regular basis might have more insight.

[Charweise]

Ah, that makes sense. The estimation works when I set the variances in the state equations equal to a small number. So now the question is, how can I estimate the variances of the time varying parameters separately from the state space regression? Stock and Watson (1998 I think) show how to do it by "inverting" a test for parameter constancy. I can replicate their results for a model with one time-varying parameter, but not for a model with more than one. Do you have any knowledge of the Stock and Watson method and/or programs that implement this method?

[nuramirah]

can anyone help me..what should i do if i want to develop tvp model from adl model.
This is my adl model: y = 0.074061 + 0.351637x1 + 0.514723x2 + 0.00000819x3
What command should i specify in the state space object?
Really need this problem solve..tq