The methods you are describing appear to be time series. If so they have little to do with the terms you referenced from the play list. Normally you are not conducting statistical test with a time series you are forecasting future values. While assumptions supposedly exist they get little attention in the time series literature (for univariate models such as Box Jenkins or its multivariate equivalent ARIMAX) or for ARMA. ARIMA is Box-Jenkins (the statisticians you popularized this approach). For regression based time series this is not true, but aside from economists I don't think many use regression based time series (examples of this are VAR, error correction models, and ARDL). They are much more likely to use univariate models notably ARIMA.

Time series is one of, if not the, most difficult type of statistics and the approaches you mention are among the more difficult in time series, because they are as much an art form as science. Worse real world data rarely matches the training that university courses provide for this. ARIMAX is incredibly time consuming, because you have to difference and determine the MA and AR order of each variable in the model.

Personally I think you would be better off to start with exponential smoothing, such as Holt Winston, rather than learn ARIMA. The forecast results are similar in terms of accuracy I believe and its infinitely easier to use.

This is as good a start as any for ARIMA. Note that I have a huge collection of such links and books - and still have not been brave enough to run it outside class.

https://people.duke.edu/~rnau/411arim.htm