Questions related to the article on Multivariate Vector Auto Regression using Python

Hi Aishwarya,
Thanks a lot for your post on Multivariate TS using VAR model(
Could you please clarify me the below questions which can help me solve many issues of my current Multivariate TS problem am working on?

1)In this article, stationarity is checked by coint_johansen test and then model is fitted. But, it wasn’t mentioned if the differencing was done or not like y(t-1). If it’s done, don’t we need to re transform the series back to original scale as the model is applied on differenced series and the values won’t be in same scale?

2)How do we know that the model VAR is of the lowest AIC? because the model is not supplied with any order number like VAR(2) or VAR(3) etc. For ex: for VARMAX, we can manually run a loop and find the lowest AIC value and pass as parameter order=(). Can we pass a desired value to the VAR model just like VARMAX?

3)After the model is fitted, there are no checks done to see if the residuals are not correlated and there is white noise only. This is normally done in ARIMA/VARMAX models using built in method “plot_diagnostics()” which prints histogram, q-q plot etc. But, here I don’t see any such check done and the 'plot_diagnostics() method seems to be not available in VAR model. So, how do we make sure that the underlying assumption is true?

4)How to interpret the RMSE values of predicted vs actuals in validation set? The numbers for some of them are way too less and for some of them are way too high. Is there not any way to print the forecasted values in the same scale as original series so that we can easily verify how close are the numbers?

Appreciate if you could clarify my above questions with the relevant code if possible at the earliest.
Thanks a lot!

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