I'm running an ARIMA model with an exogenous variable in statsmodels and I'm attempting to make predictions for multiple steps ahead without knowing the future value of the exogenous variable. The exog option in results.forecast() requires out of sample values. I'm wondering if it's possible to make forecasts for multiple days ahead without knowing these values?
In case the question is unclear, suppose I'm modeling my IQ as a timeseries variable with years of schooling as an exogenous variable. I train the model through the end of high school and I want to forecast my IQ 4 years later, but I don't know if I'll continue school or not. Can I use statsmodels to make a forecast without knowing the years of school I'll have? Thanks!
No, you must provide updated exog values to forecast out of sample. Your forecast will then depend on the values you provide.
In your example, you could produce a forecast under the assumption that you continue school or a forecast under the assumption that you didn't. Those are different scenarios and will lead to different forecasts. But the ARIMA model for IQ can't forecast whether or not you will stay in school.
You can take a look at the discussion here for some more details.