[R] Anyone Familiar with Using arima function with exogenous variables?

[Richard A. Bilonick]

Paul Gilbert wrote:

>> So if I have 200 observations and I want to estimate for time t = 
>> 201, I would use y[200] and x[200] and I would have my forecast. But 
>
> ^^^^^^
> Don't you mean x[201] ?
>

Yes, I meant x[201].

I found what I was looking for (although it's not in the R 
documentation). When Y is differenced, fitted by an AR(1) with one 
exogenous variable with no intercept, the model is written as:

(1-B)Y[t] = wX[t] + e[t]/(1 - phi B)

Solving for Y[t]:

(1 - phi B)(1 - B) Y[t] = w(1 - phi B) X[t] + e[t]

(1 - phi B - B + phi B2) Y[t] = w(X[t] - phi X[t-1]) + e[t]

Y[t] = (1 + phi)Y[t-1] - phi Y[t-2] + w(X[t] - phi X[t-1]) + e[t]

So the 1-step ahead forecast is:

Y[t]' = (1 + phi')Y[t-1] - phi' Y[t-2] + w'(X[t] - phi' X[t-1])


Rick B.