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  • What is a stationary VAR (vector autoregression)?
  • Can a VAR with non-stationary variables be stationary?
  • How do you test whether a VAR is stationary or non-stationary? (Example in R language if possible/applicable).
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  • What is a stationary VAR?

I don't think the question is correct. VAR (Vector Autoregression) is an econometric technique used to model the relationship between time series variables. We cannot say that VAR is "stationary". You can have "stationary" time series, but not "stationary" VAR models. This is not correct to say! Anyway, a stationary time series variable is a variable which fluctuate around its mean (or its trend) over time. The series may deviate for a little while but it will definitely revert back to the mean or the trend later.

  • Can a VAR with non-stationary variables be stationary?

Again the question is not formulated correctly. But this is what you want to know. Non-stationary variables can have a stationary relationship. It means that they "move together" over time. We say that they are "cointegrated".

  • How do you test whether a VAR is stationary or non-stationary? (Example in R language if possible/applicable).

In order to test whether a variable is stationary, you can use a unit root test such as the Dickey-Fuller (DF) test. In R, the tseries package contains the adf.test function.

You may want to read this. It may be a little hard to digest, but there a few easy-to-understand illustrations that will help you understand.

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