I have the monthly number of patients in a psychiatric facility from Jan 2010 to Dec 2018 - the data shows a seasonal pattern. I want to forecast the number of patients in the facility from Jan 2019 to Dec 2020 using seasonal ARIMAX, with the number of people receiving a mental health diagnosis as an exogenous variable. I have the monthly number of people receiving a mental health diagnosis from Jan 2010 to Dec 2018 also, but obviously I don't know what the future numbers will be out to Dec 2020. So first I ran a seasonal ARIMA on the diagnosis data to get predictions from Jan 2019 to Dec 2020, and then I used these predictions for the exogenous variable component of the seasonal ARIMAX model (0,1,1)*(0,1,1)12 to forecast patient numbers at the psychiatric facility over the same time period.
Is this a reasonable approach to take?
What is the ARIMAX model actually doing with the exogenous variable predictions I feed into it? Is it treating them as known values (which they are not), or does it incorporate some measure of uncertainty for these in its predictions.