Is it fine to choose 0 lag for adf test in my data? The level values weren't stationary so I took percent changes $(P_t-P_{t-1})/P_{t-1}$. Here's the data:


These are the PACFs to determine lags. I think the lag can be 0, or 7 or 11 in case of GDP and it must be 0 for MVA.

From the p-values (2nd value in bracket) I can conclude that both are stationary. But when I take higher lags for GDP (like 7) I got non-stationary. MVA seems to be stationary for all lags. What should I do? Should I take that high lag or not?


I plan on building a VAR/VEC model from hereon to check for granger causality.
 A: 1.)
Please look into these vids:
VAR with Python
https://www.youtube.com/watch?v=6Ye0CsfRDJg
AR orders in general
https://www.youtube.com/watch?v=5-2C4eO4cPQ
2.)
There you can see that we normally ignore lag 0 in a PACF. A lag of 0 for a series with itself would mean you would explain the time series by itself with no shift. That doesnt make sense, as you would explain the series by an exact copy of it. So you have to go to higher lags in generall when interpreting PACF. Now to the ADF.
3.)
It is possible that the ADF test tells you, that at later parts a series is no longer stationary. See here: (but for R, but it deals with the theory) https://www.r-econometrics.com/timeseries/stationarity/. And that means yeah it is no longer stationary. Going with higher lags also doesnt mean, that these will be significant in the end for a VAR as you see in the vids.
4.)
If one variable is stationary and the other is not at lag 7. You should transform both variables with log and differences for VAR in differences. As you
not mix up transformations and non transformations in a VAR
5.)
In general you could do:

*

*a VAR in levels (if all features are stationary)

*a VECM, transforming no variable and checking for unit root (that would be still one chance for you to circumvent transformation and use lag 7 without transformation

*VAR in differences, a VAR with transformed variables

Update
not really the same as percentage change

