Modeling the error variance in a state space model

[miksterz1]

Hello,

I have been through the user guide and am able to estimate state space models quite comfortably, but have not been able to figure out how I can posit a dynamic process for the error variance.
For instance, consider the following simple model:

@SIGNAL y = trend + [VAR=EXP(C(1))]
@STATE trend = trend(-1) + [VAR=EXP(C(2))]

What I would like to do is have the error variances from both the signal and state equation follow random walk processes. Would appreciate if anyone could help point me in the right direction.

[trubador]

I presume you are referring to disturbances. If so, then all you have to do is specify it as an additional state variable:

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@signal y = sv1*x + res
@state sv1 = sv1(-1) + [var=exp(c(1))]
@state res = res(-1) + [var=exp(c(2))]

You should keep in mind that random walk is an extremely flexible specification and therefore it may not allow you define additional dynamics. For instance, following is an ill-defined specification and you'll probably experience identification problems:

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@signal y = level + res
@state level = level(-1) + [var=exp(c(1))]
@state res = res(-1) + [var=exp(c(2))]

[miksterz1]

Ah, I had a feeling the solution was something along those lines. What I am after is an unobserved components model with stochastic volatility such as in Stock and Waton (2006). I see why that example you gave wouldn't work. However, I just realized that the variance of the disturbance actually need to be modeled as ln(variance) = ln(variance(-1)) + error.

[trubador]

Yes, but unfortunately that leads to other difficulties. Please see the following discussion: viewtopic.php?f=4&t=6744h However, you can try the recursive approach outlined here: viewtopic.php?f=4&t=7110&p=25109