- 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
Rlanguage if possible/applicable).
where $\Phi_i$ are matrices and $\varepsilon_t$ is white noise process. If the process satistfying this equation is stationary we say that the VAR is stationary. Given matrices $\Phi_i$ you can test whether the solution is stationary or not. If the roots of the following equation are in modulo greater than 1, then the solution is stationary:
where $|A|$ is the determinant of matrix $A$.
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.
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".
In order to test whether a variable is stationary, you can use a unit root test such as the Dickey-Fuller (DF) test. In
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.