# [R] FW: RE: arima and xreg

markleeds at verizon.net markleeds at verizon.net
Wed Sep 10 18:13:59 CEST 2008

```  hi: you should probably send below to R-Sig-Finance  because there are
some econometrics  people over there  who could also possibly  give you
a good answer and may not see this email ? Also, there's package called
mar ( I think that's the name ) that may do what you want ?

Finally, I don't know how to do it but I think there are ways of
converting a multivariate arima into the equivalent state space form and
then you could estimate it that way using dse, dlm etc but that's as far
as i'll go there because the univariate  conversion case is complicated
enough and i've never considered the multivariate  case. good luck.

On Wed, Sep 10, 2008 at 10:36 AM, Jose Capco wrote:

> Dear R-help-archive..
>
> I am trying to figure out how to make arima prediction when I have a
> process involving multivariate time series input, and one output time
> series (output is to be predicted) .. (thus strictly speaking its an
> ARMAX process).  I know that the arima function of R was not designed
> to handle multivariate analysis (there is dse but it doesnt handle
> arma multivariate analysis, only simulations). But there is this
> beautiful "xreg" as parameter for arima and I was wondering..
> for the case of one output series I can actually "trick" R in doing
> multivariate time series for me no?.. because I saw in the
> documentation, xreg can be inputed as a ---matrix--- with output.len
> (length of output data) number of rows.. So in fact I can let the
> different columns of xreg to actually be the different input time
> series I need!
>
> Is anyone familiar in how arima with xreg as given estimate models? ..
> how is the model assumed?
>
> supposing I write :
>
> arima(y, xreg=U, order=c(3,0,2))
>
> how is y_t calculated? (supposing U has 2 columns, with U[1] being
> first column and U[2] second column)
>
> is it
>
> y_t = theta_(t-1)y_t-1 + .... + theta_t-3 y_t-3 + intercept + U[1]_t +
> psi[1]_t-1 U[1]_t-1 + psi[1]_t-2 U[1]_t-2 + ....+  psi[2]U[2]_t-2 +
> e_t + phi_t-1 e_t-1 + phi_t-2 e_t-2
>
> ??
>
> e_t .. etc. are the white noise series of the model.
>
> the documentation is totally vague when it comes to xreg. I hope it is
> like above :)
>
> Would appreciate any remarks or comments. Thanks in advance.
>
> Sincerely,
> Jose
>
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