ARIMA forecasting using exogenous variables with their own forecast intervals

Question

Suppose

model <- Arima(y , xreg=cbind(x1, x2), order=(p,d,q))

If I am forecasting $x_1$ and $x_2$, then for forecasting $y$:

1) If I use expected forecasts for $x_1$ and $x_2$ (single numbers), I simply do:

forecast(model, xreg=cbind(E(future x1) , E(future x2))

2) How about if I want to use forecast intervals for $x_1$ and $x_2$?

This post suggests that: you can draw (a lot of) random numbers from each predictive density, plug them into the model and get a predictive distribution for $y$. Then I guess taking the average prediction interval to come up with the one forecast interval for $y$. Does this make sense?

Answer 1

Generate a family of forecasts for each point in the future for all input series allowing for identified unusual values in the past of all input series to have an effect on the forecasts for these exogenous series. Then introduce these exogenous robust forecasts into the regression model perhaps with appropriate lags and any needed ARIMA structure. Enable unusual/identified activity in the history of Y to rubustify the forecasts for Y.