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Don't all the variables used have to be of the same order of integration in VAR models ? In this paper Bayesian VAR Forecasts, Survey Information and Structural Change in the Euro Area Gergely Ganics and Florens Odendah are using $\Delta$loglevel, loglevel and level data as we can see on page 28 (31).

Thank you in advance for the clarification !

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  • $\begingroup$ That does not automatically mean the transformations of variables that are used are not integrated of the same order. $\endgroup$ – Richard Hardy Aug 28 at 10:52
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    $\begingroup$ I’m voting to close this question because it is not about Quantitative Finance and would better fit on Cross Validated or Economics SE. $\endgroup$ – Richard Hardy Aug 28 at 10:54
  • $\begingroup$ Ok thanks for your first answer, but I don't see how log level oil price would be integrated of the same order... I posted it there because I want to use BVAR to forecast some sectoral indices, but fair enough to close it if you think it doesn't fit there. $\endgroup$ – Jur Aug 28 at 11:17
  • $\begingroup$ My points is, without knowing what variables there are and what their orders of integration (before any transformations) are it is impossible to tell whether their transformations as used in the BVAR are integrated of the same order. This is just a technical point. But in the concrete application you have in mind, your concern may be relevant; more information is needed to tell that. $\endgroup$ – Richard Hardy Aug 28 at 11:22
  • $\begingroup$ "The column Transformation indicates which variable entered the model in levels, log-levels or in log-differences", it's quite clear that they used datas from different integration orders to me, and I checked the data on AWS they are on level. Anyway I was just curious, I don't think I will use data from different order of integration. $\endgroup$ – Jur Aug 28 at 11:26
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So I asked on reddit, and got this answer from Rasseren :

The integration order of the endogenous variables is most often used to ensure reasonable stability (all eigenvalues of the companion form <1 in modulus) of the process; remember stability implies covariance stationarity in theory.

There is nothing, except maybe the underlying theoretical model e.g. Taylor-rule, prohibiting differing integration orders. In fact, most high-profile VAR studies utilizes different integration orders, see e.g. Stock & Watson (JEP, 2001), Bernanke et al. (Quarterly Journal of Economics, 2005) even the seminal studies of Christopher Sims (1972,1980).

The difference lies only in the interpretation of coefficients and IRFs (growth rates vs. level effects).

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