What I'm dealing with here VAR, VARX or something different?

I have to implement a time-series tool in my company, and I'm not sure what I'm dealing with, when looking at the old tool. We have one target variable (sales) and a lot of different independent variables (e.g. spendings or amount of new users).

My coworkers are used to work with an automated blackbox-tool. When they are done 'modeling' they get something like a block of equation terms (screenshot). That consists of a curve fitting transformation to the equation term and the lag of the current series or independent variable. The goal of the modeling is forecasting sales with a holdout set.

The tool itself works with a genetic algorithm, which allows the modeler to steer population and mutation rate only.

I have two questions, and I hope you can help me:

1. I know how the concept of lags works, and I know to do curve fitting in R. However, what I really don't know is, what I'm seeing. Are these independent variables just an 'illusion' and we are dealing with a vector automated regression? Or is it just simpler or more complicated, are these independent variables the x from the VARX?
2. The second question is a general one about hold-out sets. We often have several years of data which we should model n a weekly base, e.g. three years of data result in 156 data points in the tool.
However, we usually have campaigns which are only active 4-6 weeks in one year and not in the other two years, thus we have variables that are only active in a certain time period. How do we deal with that?
My coworkers still integrate them, although this result in a bad fit for the test data.
How is it possible to integrate a variable that is only active such a short weeks in such a long time series, when we have to do work with a hold-out set? Is there an alternative to the holdout approach?

• vector automated regression? VAR stands for vector autoregression, where auto- does not indicate automation; rather, it indicates self- (like in autoportrait), i.e. regression on lagged values of the variable itself. – Richard Hardy Sep 8 '20 at 8:59
• @Richard, sorry that was just a typo. Would it be possible to get a similar solution with a vector autoregression? – Patrick Sep 8 '20 at 10:50
• Please register &/or merge your accounts (you can find information on how to do this in the My Account section of our help center), then you will be able to edit & comment on your own question. – gung - Reinstate Monica Sep 8 '20 at 13:13
• I don't know how to answer 1 with the results presented, you really need the equation or software they ran. For 2 it looks like you are running ARIMA or something like that. I think you might consider segmented regression instead which looks at the impact of an intervention over time. It does not require stationarity (or at least I have never seen that suggested, almost by definition an intervention should generate non-stationarity). This will show the result of the intervention, it is not a time series. – user54285 Sep 11 '20 at 17:31