I'm forecasting a timeseries that has both trend and seasonality component, which is why I am using ARIMA. Without providing external regressors, the best model selected (in training) has the following order:
ARIMA(3,0,0)(2,1,0) with drift. When allowing re-estimation in forecasting, the most selected order ist
ARIMA(1,0,1)(2,1,0) with drift. This is all fine and performance on the test set is good.
Now I want to check, whether the forecast accuracy increases when adding external regressors. I'm working with macro-economic factors and I'm facing the following challenges:
- Multicollinearity - high correlation between predictor variables. It is not of importance though to separate the impact of each predictor, so as I read in FPP (https://otexts.com/fpp3/causality.html) it shouldn't be that problematic, right?
- Since I'm working with macroeconomic indices, do I need to make the regressor variables stationary before adding them as predictors? Right now I'm facing the issue that the values of the future predictors (test set) are out of range when comparing to historical values because they obviously follow a trend.
When comparing the results of a regression model with ARIMA errors, the performance is worse than without regressors, which might be due to the future regressors being out of the range of historical values (not all the time but at some point, especially when considering corona times as well).
Does unreliability of the forecast increase with the number of values being out of range?
Would differencing the predictor series help? Does it even make sense to include a variable that is seasonally adjusted as predictor for a seasonal time series?