Predicting 2 steps ahead with ARMA

Asked Dec 28 '21 at 19:07

Active Dec 28 '21 at 19:29

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How does one forecast 2 steps ahead in an ARMA model? If my training data is $y_1, ..., y_T$, and I have an ARMA(1, 1) model, then I have

$$\hat{y}_{T+1} = \alpha*y_T + \beta*(\hat{y}_T-y_T)$$

but what about $\hat{y}_{T+2}$? How would I know what to multiply $\beta$ by, because I don't know the error at time step $T+1$?

edited Dec 28 '21 at 19:29

Richard Hardy

asked Dec 28 '21 at 19:07

ignoring_gravity

Does this answer your question? [Multistep prediction interval for ARMA(p,q) process](https://stats.stackexchange.com/questions/352840/multistep-prediction-interval-for-armap-q-process). (The linked thread covers your case even though its title does not immediately suggest so.) – Richard Hardy Dec 28 '21 at 19:29
So in this example, the \beta term would disappear, if we plug the forecast for T+1 in place of the true value, right? – ignoring_gravity Dec 28 '21 at 19:31
1

Right. The point forecast of a future error term is zero. – Richard Hardy Dec 28 '21 at 19:32
perfect, thanks! – ignoring_gravity Dec 28 '21 at 19:33

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