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I have a stationary and a non stationary time series. For estimating a VAR model, both time series should be differenced or only the second?

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VAR estimation requires both the series to be stationary or to be cointegrated (to avoid spurious results). If, after proper hypothesis testing (unit root or stationarity tests), the first series results to be stationary, you can use it as it is (I use the word "can" because, depending on what are you studying, maybe you can be interested to study also the relationship between the two series both differentiated). The second must be differentiated one or more time to be stationary. Be careful, after differentiating the series you must interpret correctly the new output.

I quote a passage from Hill, Griffiths and Lim, Principles of Econometrics, Chapter 13:

To recap: the VAR model is a general framework to describe the dynamic interrelationship between stationary variables.

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  • $\begingroup$ Thank you very much.After differentianting the second time serie it will have an element less than the other.Can I estimate a model if the variables havent the same observations number?When I choose the lag length I will also use the differentiating time series?Can you suggest me some link or exapmles of VAR applications.Thabk you so much.@Kolmogorovwannabe $\endgroup$
    – Eni
    Commented Dec 26, 2018 at 11:59
  • $\begingroup$ Depending on the program that you are using, it will automatically deal with missing observations (generally programs shorten the series so that each series have the same number of observations). If you don't want to miss that observation, you have to enrlarge your series. The lag lenght can be carried out using the differentiated series. To estimate the model I suggest to you econometric softwares, such as Eviews or Stata (or other free use), they are easy to use and their outputs are easily interpretable. You can find dozens of tutorial on you tube for example digiting "VAR model Eviews". $\endgroup$ Commented Dec 26, 2018 at 12:43
  • $\begingroup$ Thank you very much.Your answers help me!I am using r , vars package. $\endgroup$
    – Eni
    Commented Dec 26, 2018 at 12:53
  • $\begingroup$ It is a very good package! You're welcome. $\endgroup$ Commented Dec 26, 2018 at 16:11

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