I'm having some difficulty applying concepts I'm learning about Transfer Functions into useful equations. I've read a couple of the related posts, and perhaps I need to learn by example... I have two examples below, which are output from made-up data in SPSS Time Series modeler. As I am simply trying to learn the mechanics of Time Series, and how the equations work, I would like it if someone could walk me through translating the output into an equation I could understand and manipulate in Excel. I understand that SPSS produces the forecasts automatically, but I'm trying to better understand the mechanics. Any help is appreciated.
One of the thorniest issues in transfer function modelling is the lack of clarity when the results are presented. AUTOBOX takes the final model and expresses the forecast in "regression-like terms) i.e. an explicit equation showing an understandable ( to the layman ) presentation. This is a unique feature and is referred to as RHSIDE.TXT for your second example.
For your first example ..using data you had provided in ARIMA with independent variables I obtained for RHSIDE.TXT a presentation that expressed the forecast in terms of the Y and the one input and the history of errors. This was obtained by multiplying through by the denominator structure for X where VAR1 is your APPLES.
I suggest that you ask SPSS to provide this useful report for you and others struggling with understanding the model in simple terms. Note that the re-expression can get "complicated" with either denominator transfer function structure structure or arima model structure ... which perhaps is why SPSS doesn't present it.