The RATS Software Forum

fan wrote:Hello,
I am using state space techniques for the 1st time, I have a model but I am not sure how to represent it in state space form.

Here is my model: the measurement equation is Yt=B0X0,t+B1X1,t+B2X2,t+Ut and the transition equation is X2,t=Ct+X2,t-1+Dummyt+Et. X0 and X1 are the exogenous variables and X2 is the unobserved state.

Any help is deeply appreciated.

TomDoan wrote:

fan wrote:Hello,
I am using state space techniques for the 1st time, I have a model but I am not sure how to represent it in state space form.

Here is my model: the measurement equation is Yt=B0X0,t+B1X1,t+B2X2,t+Ut and the transition equation is X2,t=Ct+X2,t-1+Dummyt+Et. X0 and X1 are the exogenous variables and X2 is the unobserved state.

Any help is deeply appreciated.

Use the MU option to handle the B0 x X0 + B1 x X1, the Z option to handle the C+Dummy in the transition. As you have that written, you'll need the variance of E to be pegged to 1 to avoid a lack of identification between B2 and that variance. See harveyp393.rpf for an example of the use of MU.

TomDoan wrote:No. Kim and Nelson really focus on MS models, so the state space examples are rather simple. The Harvey example isn't that hard to figure out just from the code.

fan wrote:

TomDoan wrote:No. Kim and Nelson really focus on MS models, so the state space examples are rather simple. The Harvey example isn't that hard to figure out just from the code.

Dear Pro. Doan Thank you for the reply. I looked the code of the example. I think I get the basic idea about what the example tries to show. However, I still have questions about some details and I am seeking for your help. Correct me if I am making mistakes, please.

Basically, the estimation model for the example is that
Unemplt=trendt+Unemplt-1+output+output-1+output-2+Et
Trendt=trendt-1+trendratet+Ut
Trendratet=trendratet-1+Vt

fan wrote: frml(reg, vectpr=b) linereq
#empl{1} output{0 1}
Compute b=%zero(3,1)
These are codes ask Rats to run a simple linear regression for unemployment on its own lag and the output, output lagged once and output lagged twice and calculate the coefficients on three explanatory variables and store them in b.
I want to make sure whether b=%zero(3,1) means keep none-zero elements in a 3x1 vector.

@localdlm(type=trend, shocks=both, a=at,c=ct,f=ft)
This code is for the only state variable in the model (trend).

Nonlin sigspeps sigsqeta sigsqzeta b
This code is to specify the coefficients we are interested about. Sigspeps=var(Et), sigspeps=var(Ut) and sigsgzeta=var(Vt)

Compute sigsqeps=.5*1.e+4*%seesq, sigsqeta=.01*sigsqeps, sigsqzeta=sigsqeta
I am not too sure what this code for. Could you please explain it to me? The tip says that the variances have a naturally very small magnitude, so we force the estimated versions to be 4 orders of magnitude larger.

fan wrote: dlm(a=at,c=ct,f=ft,mu=lineareq,sv=1.e-4*sigsqeps,sw=%diag(||1.e-4*sigsqeta,1.e-4*sigsqzeta||),$
exact,y=empl,method=bfgs,vhat=vhat,svhat=svhat,type=smoothed) 2 * xstates
I know this is code for running state space model in Rats. However, I am not sure why sv=1.e-4*sigsqeps,sw=%diag(||1.e-4*sigsqeta,1.e-4*sigsqzeta||) and 2 * xstates. Could you please explain it to me?

fan wrote: set stdu 2 * = %scalar(vhat)/sqrt(%scalar(svhat))
This is code for generating stud2.

@STAMPdiags stdu
This is code for running state space model diagnostics on stud.

I am terribly sorry for asking so many questions to you at once. I am looking forward to hearing from you soon.

Best regards,
Fan

TomDoan wrote:

fan wrote:Hello,
I am using state space techniques for the 1st time, I have a model but I am not sure how to represent it in state space form.

Here is my model: the measurement equation is Yt=B0X0,t+B1X1,t+B2X2,t+Ut and the transition equation is X2,t=Ct+X2,t-1+Dummyt+Et. X0 and X1 are the exogenous variables and X2 is the unobserved state.

Any help is deeply appreciated.

Set trend = X2
dec frml zf[vect] zf
frml(reg,vector=b) lineareq Y
#X0{0} X1{0}
compute b=%zero((2,1)
@localdlm(type=trend,shocks=trend,a=at,c=ct,f=ft)
nonlin sigsqeps sigsqeta b d
Frml zf = ||constant+d*dummy||
dlm(a=at,c=ct,f=ft,mu=lineareq,z=zf, sv=1.e-4*sigsqeps,sw=%diag(||1.e-4*sigsqeta,1.e-4*sigsqzeta||),$
  exact,y=Y,method=bfgs,vhat=vhat,svhat=svhat,type=smoothed) 2 * xstates

fan wrote: Dear Tom, These are codes in my mind for my model. I am sure there are many mistaks, Could you please kindly point out them for me?

Code: Select all

Set trend = X2
dec frml zf[vect] zf
frml(reg,vector=b) lineareq Y
#X0{0} X1{0}
compute b=%zero((2,1)
@localdlm(type=trend,shocks=trend,a=at,c=ct,f=ft)
nonlin sigsqeps sigsqeta b d
Frml zf = ||constant+d*dummy||
dlm(a=at,c=ct,f=ft,mu=lineareq,z=zf, sv=1.e-4*sigsqeps,sw=%diag(||1.e-4*sigsqeta,1.e-4*sigsqzeta||),$
  exact,y=Y,method=bfgs,vhat=vhat,svhat=svhat,type=smoothed) 2 * xstates

Furthermore, I am not sure how to peg the variance of E to 1, Could you please show me how to do that?

TomDoan wrote:

fan wrote: Dear Tom, These are codes in my mind for my model. I am sure there are many mistaks, Could you please kindly point out them for me?

Code: Select all

Set trend = X2
dec frml zf[vect] zf
frml(reg,vector=b) lineareq Y
#X0{0} X1{0}
compute b=%zero((2,1)
@localdlm(type=trend,shocks=trend,a=at,c=ct,f=ft)
nonlin sigsqeps sigsqeta b d
Frml zf = ||constant+d*dummy||
dlm(a=at,c=ct,f=ft,mu=lineareq,z=zf, sv=1.e-4*sigsqeps,sw=%diag(||1.e-4*sigsqeta,1.e-4*sigsqzeta||),$
  exact,y=Y,method=bfgs,vhat=vhat,svhat=svhat,type=smoothed) 2 * xstates

Furthermore, I am not sure how to peg the variance of E to 1, Could you please show me how to do that?

I'm not sure what the set trend = x2 is supposed to be doing. The "trend" is estimated as part of the calculation.

This

dec frml zf[vect] zf

should be just

dec frml[vect] zf

compute b=%zero((2,1)

has an extra (

What is ZF supposed to be doing? The Z is a shift in the state transition model, so it needs to be a 2-vector to match the number of states.

Other than the ZF, this looks correct. You don't need to peg any of the variances as (unlike the first =equation you posted), you don't have a constant multiplier on the state-space trend---you just have that adding on.

TomDoan wrote:I'm confused about this:

X2,t=Ct+X2,t-1+Dummyt+Et (transition equation)

What are Ct and Dummyt supposed to be? Is X supposed to be a drifting random walk where the drift changes? If so, why do you have no parameters? Is the drift a rate of 1 for the non-dummied sample and 2 for the dummied part? That's how you wrote that. Is the local trend model something you copied from the Harvey example, since as you have this written, you don't want that?

TomDoan wrote:I'm confused about this:

X2,t=Ct+X2,t-1+Dummyt+Et (transition equation)

What are Ct and Dummyt supposed to be? Is X supposed to be a drifting random walk where the drift changes? If so, why do you have no parameters? Is the drift a rate of 1 for the non-dummied sample and 2 for the dummied part? That's how you wrote that. Is the local trend model something you copied from the Harvey example, since as you have this written, you don't want that?

TomDoan wrote:First of all, it would be helpful if you typed RATS commands into RATS itself, instead of into a word processor or whatever you're using. Things like the ||'s are being translated into non-standard characters.

Also, you can attach GIF files for formulas, as in:

The attachment formula.gif is no longer available

The "constant" is a free parameter, isn't it? You didn't allow for that. The A is also a free parameter. With your model, the A "matrix" would be just A, the C matrix would be just 1.0. Z is C+D*DUMMY. You don't need F since you have just the one state. SW is a single parameter, not a matrix. So in total you have A, C, D, the regression parameters, and the two variances as your free parameters.