This is tricky. First of all, most theoretical model tell you that the data is stationary. The big question is whether the empirical data satisfy that requirement. Most people tend to say yes for many countries and therefore do not rely on formal statistical tests. After all, we all know the problems with low power of tests in short data and problems like structural breaks etc. There is also the problem of near unit-root behavior. The latter is regularly assumed to be the reason of the persistence in inflation, i.e. the central bank having a slow-moving inflation target.
Regarding VARs, there is the Sims/Stock/Watson result. See Is the effective federal funds rate stationary? - #2 by jpfeifer
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