[R] Constructing a VAR model using dse
Paul Gilbert
pgilbert at bank-banque-canada.ca
Wed Aug 4 15:23:50 CEST 2004
Wolfgang Abele wrote:
> Hi everybody,
>
> I'm trying to construct a VAR model where the output variables can influence each other in the same time period, for example:
>
> x1_t = ax1_t-1 + bx2_t-1 + e1
> x2_t = cx1_t + dx2_t-1 + e2
>
> So x2_t is influenced by x1_t.
>
> Does anybody know how to construct such a model using the dse package?
>
> If I write AX = ... I know I could get rid of the A matrix by multiplying both sides with the inverse matrix A^(-1). Does this method always work or is it restricted to certain cases of the covariance matrix E?
It almost always works. (There are lots of difficulties in multivariate
time series, but not because of this.) If A is singular then there is a
problem, but there is also a problem with your model in that case.
Almost all estimation procedures impose the restriction that the model
has been made identifiable by multiplying by A^(-1). (Your A is often
called A(0), the zero lag coefficient of the AR polynomial matrix.) If
this restriction is not made, then some other identifying restriction
has to be imposed.
If you know A because of some physical understanding of the system (i.e.
the coefficient c in your equations above) then you can estimate in the
usual form and recover the form you would like by multiplying through by
A afterward.
Paul Gilbert
>
> Thanks a lot for your help!
>
> Wolfgang
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