[R] arima and xreg

[Jose Capco]

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