[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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