1-Can I run my VAR model on first differenced or percent return? or should it always be on the level, whether there is cointegration or not?
2-If i'm running another VAR model on the level, shall I take the logs?
1. You should use the stationary version of the variables in a VAR, so if I(1), use the difference or percent return. If there is cointegration, you can use the VECM option
2. A log transformation is useful in linearizing a relationship, and also easing interpretation of changes variables with widely different scales (GDP in dollars vs. a price index, for example). However, this consideration is secondary to the stationarity question.
Michael R Jonas thank you for your help.
So if I understand correctly it’s not wrong to use the differences or returns stationary variables, correct?
thre only downfall would be that I will be using VAR only and there will not be any cointegration relationship VECM since the variables are not in level form, correct?
This is a simple and helpful paper:
Conference Paper Comparison of vector autoregressive (VAR) and vector error c...
It is appropriate to take the natural log of a series if it exhibits exponential growth. The may be apparent from a plot where visual inspection shows larger changes and larger fluctuations at later dates.
If an exponential series is simply differenced, then the differences and the variation in the differences tend to become larger at later dates.
It’s customary and good practice when working with multiple time series to check for stationarity and cointegration.
Differencing may or may not be appropriate depending, in part, on whether or not some of series are stationary and whether or not there is cointegration. For example, it doesn’t make sense to regress a series that is not stationary on one that is (e.g. real GDP on a constant).
Also, see page 270 (in Chapter 6) of Applied Econometric Time Series by Walter Enders. A key sentence, but read the entire section to get the context and an alternative view, is: “The main argument against differencing is that it “throws away” information concerning the comovement of the data (such as the possibility of cointegrating relationships)”.
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