[R] Specifying State Space model to decompose structural shocks

[Anjan Panday]

Dear all:

Greetings!

I am trying to replicate a simple state space model in R, using the
package 'dlm'. This model has two observation equations and three
state equations. Each observation equation represents structural
shocks based on SVAR for country i, where i=1 to 2. The structural
shocks (S1 and S2) are to be decomposed into common (sv1) and
country-specific (sv2, sv3) shocks. We are interested only in the
coefficient of common shock. Moreover, the transition equation is
represented as a random noise.

Observation equation:

S1=c(1)*sv1+sv2
S2=c(2)*sv1+sv3

Transition equation:

sv1=(variance=1)
sv2=(c(3))
sv3=(c(4))

The variance (of the region-specific shock) in the first State
equation is set to 1, while the variances of second and third state
equations are to be estimated. Total four parameters to be estimated.

I have also attached the paper that uses this specification.

To specify above model in R, I am considering the dlm package, which
suggests that multivariate series can be represented by combining two
univariate expressions. First, I need to write a function and then use
dlmMLE to estimate it. For example, I can start by writing a function
x, which combines two univariate expressions:

ab<-function(x)
{
dlmModPoly()%+%dlmModPoly()
}

fit<-dlmMLE(data, parm=c(....), build=ab)

However, I am not sure how to write my model within this function. For
instance, when I just run the expression inside above function, I get:

> dlmModPoly()%+%dlmModPoly()
$FF
     [,1] [,2] [,3] [,4]
[1,]    1    0    0    0
[2,]    0    0    1    0

$V
     [,1] [,2]
[1,]    1    0
[2,]    0    1

$GG
     [,1] [,2] [,3] [,4]
[1,]    1    1    0    0
[2,]    0    1    0    0
[3,]    0    0    1    1
[4,]    0    0    0    1

$W
     [,1] [,2] [,3] [,4]
[1,]    0    0    0    0
[2,]    0    1    0    0
[3,]    0    0    0    0
[4,]    0    0    0    1

$m0
[1] 0 0 0 0

$C0
      [,1]  [,2]  [,3]  [,4]
[1,] 1e+07 0e+00 0e+00 0e+00
[2,] 0e+00 1e+07 0e+00 0e+00
[3,] 0e+00 0e+00 1e+07 0e+00
[4,] 0e+00 0e+00 0e+00 1e+07


I am wondering how do I specify the coefficient for common shock and
country-specific shocks in the FF matrix. Similarly, how do I write
three transition equations? Do I change all of the elements in GG
matrix to zero, since this is a model with pure noise in state
equation? Moreover, am I correct to use dlmModPoly to build a function
for my state space model?

Kindly suggest to help me estimate the model.


Best regards,

Anjan Panday
American University
Washington, DC
-------------- next part --------------
A non-text attachment was scrubbed...
Name: state space.pdf
Type: application/pdf
Size: 150565 bytes
Desc: not available
URL: <https://stat.ethz.ch/pipermail/r-help/attachments/20110630/c61f55c2/attachment.pdf>