I have an ARIMAX model that has AR & MA terms along with exogeneous variables at prior lags. I am predicting on a continuous process and attempting to forecast to 1 and 10 units ahead. However, the important lags for the exogeneous variables are within the 1-10 units. Thus, it fails to produce 10 units ahead forecast on the most recent data.

For example, I have a x variable with a lag of 3 (x_3) in the model. I just received the most recent result (0 units ahead).

If I forecast to 10 units ahead, that forecast requires the x_3 to be non-missing at 7 units, which isn't possible since it hasn't occurred yet. Therefore, no prediction is made at 10 units ahead.

How do I resolve this issue? Do I attempt to fit an ARIMA model to the x variables? Use the last value for x and propagate it forward? Am I using this method incorrectly? Create a new model that only uses exogeneous lags that exceed the forecast step size (x_11 for the 10 step forecast)?