I'm trying to interpret the forecast values from an ARIMAX function, and I'm confused about what's happening in the actual forecasted values as I change the values for the predictor during the forecast period.
The ARIMAX model shows one of the predictors (Spend) has the following (significant) transfer function coefficients
Numerator (lag 0)= .029 Denominator (lag 2) = .038
I held the forecast values of the predictor "Spend" constant and the compared different level - i.e. 6 periods at 100,000, then 6 periods at 200,000
One would expect that doubling the value of "Spend" would dramatically increase the predicted forecast - holding everything else constant. But it does not.
The effect was two periods of positive forecast values, followed by 4 periods of negative forecast values. I suspect this may have something to do with the denominator being larger than the numerator in the transfer function. (that's a guess). However, I also cannot explain why the forecast is positive for two periods and then goes negative, and stays negative. Why wouldn't it oscillate given the 2-period lag in the denominator?
(I've been trying to make good use of this post: Transfer function in forecasting models - interpretation)
Your help is appreciated, as always!