[Python] Stationary data for time series forecasting OLS

I am building a time-series forecasting model using OLS.

For preparation, I am making all series stationary (for now).

What I don't understand:

• Series should be stationary
• Achieving stationarity can be done through various means; including:

1. removing trend (if series is trend-stationary)
2. difference once (.diff())
3. differnce twice (.diff().diff())

I am testing stationarity by getting scores from ADF and KPSS tests.

Now, I am confused . I read that when you build OLS, your series can be transformed in different ways, since OLS looks at uni-directional relationships (dependent variable vs independent variable).

This is different for a VAR where all series are influencing each other. In this case all you series have to be transformed in the same way.

But, it doesn't sound intuitive. Basically, OLS will look at the relationship between your dependent variable and independent variable and understand how they move together. Ideally your dependent variables to carry as much information as possible that can explain how your independent variable moves.

But imagine this scenario:

• make independent variable (A) stationary (I(1)): difference once (MoM change)
• make dependent variable (B) stationary (I(2)): difference twice (Change in MoM change)
• make dependent variable (C) statinoary (I(0)): remove trend

So if you are building a model with these stationary series it feels like comparing apples with pears? It doesn't sound intuitive looking at the story of the data.

Plotting A against B: comparing MoM change vs change in MoM change Plotting A aganist C: Comparing MoM change vs keeps current values

So I;d say if I transform the series I have to transform them all in the same way? It feels like it doesnt make sense transforming in different ways, even if the data is asking for it.

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