# [R] arima and xreg

David Stoffer dsstoffer at gmail.com
Thu Sep 11 06:24:00 CEST 2008

```Your model is close, but not correct... there are no t's on the parameters
and the U's aren't lagged.

You can find an ARMAX example on our "quick fix" page:
http://www.stat.pitt.edu/stoffer/tsa2/R_time_series_quick_fix.htm .  The
example is near the bottom and just above the spectral analysis example, but
you may want to read the "regression with autocorrelated errors" example
first to get some background.

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 :)
>
>
> Sincerely,
> Jose
>
> ______________________________________________
> R-help at r-project.org mailing list
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> and provide commented, minimal, self-contained, reproducible code.
>
>

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