I am running a VAR with a single stock price and a sentiment measure as endogenous variables, and the DAX, the IMX (real estate index), industry turnover, wages and unemployment as exogenous variables.
As there are different methods to transform my variables to be stationary, I am not sure, which one is adequate to use.
I either
(1) use continous growth rates meaning e.g. logdax t - logdax t-1
(2) use differences, e.g. dax t - dax t-1
When applying growth rates, unfortunately industry turnover and unemployment are still not stationary (well they are in the ADF test, but not for trend&intercept, but only for "Intercept" and "none" - is this enough?). So I would use differences for those (even the second one for unemployment, as the first one does not make the time series stationary yet).
Can I use different transformation methods within one model? So for example growth rates for DAX and IMX, and differences for the rest or is this not recommended?
Best,
Franziska
Hello,
1- Yes you can use different transformation methods ( but beware when interpreting the estimation results)
2- A not for log transformation, In time series analysis, this transformation is often considered to stabilize the variance of a series , but an effect on forecasting is likley to happen.
3- For industry turnover and unemployment , check if you have not a structurla break in your time series.
4- I final remark, why you deal with VAR model when you just put one endegenous variable ; I think it's equivalent to run a multiple regression model.
Best wishes
Thanks for your answer!
A quick follow up question: when interpreting the results of differently transformed variables, the Granger causality and lags should stay the same right? Because I cannot interpret the coefficients anyways in VAR...
I have two dependent variables, this is why the VAR seemed most appropriate :)
so normal growth rates (Dax t - dax t-1/Dax t-1) should work, just log growth rates (log dax t - log dax t-1) not, correct? I am just wondering as a read that the continuous log growth rate is the better one as it deals better with assymetries in positice and negative growth rates...
thanks a lot!
Yes, it is not a problem to use different transformations for variables.
For DAX, you should without hesitation use:
(1) use continous growth rates meaning e.g. logdax t - logdax t-1
For the rest, use economic intuition. For example, for unemployment, I would use simple differences:
(2) use differences, e.g. unemployment t - unemployment t-1
There is no effect on Granger causality test;
However, the most important in VAR models (or VARX(p,s) in your case) is certain functions that have some economic meaning and, hopefully, are more precisely estimated. Among the many possible functions: impulse responses, variance and historical decomposition.
Regards
Thanks a lot for your answers to both of you, very well explained!
Can I add one more question: in the ADF test, which of the three variations should I listen to for
- DAX
- IMX (German real estate index)
- industry turnover
- unemployment
- wages?
To the version (1) intercept, (2) intercept & trend or (3) none?
Thanks a lot!
I think Franziska Weis , Firstly, you have to familiarise with basic time series analysis, statioanirty process , ... because according to your question, it's the basic method of unit roots tests used for test and make stationaire time series.
try structural break unit root and cointegration tests to determine the time series properties of variables! If you end up finding mixed of diffrenet degree of integration of variables, please try ARDL Bounds testing apprach! Good luck!
Mustafa
1. Using logs: The main reason for using logs in econometric models is to put the variables in the same scale. E.g. If a stock price (P) is measured in dollars and the employment (E) is measured (of course) in persons or percentages, then a regression between P and E, without logs, will be meaningless. And, if you use one variable in logs, for consistency, then it's better to use all of them in logs. I believe this answer the "logDax vs. Dax" dilemma.
2. Using first differences: Indeed, using first differences of a non-stationary variable - I(1) variable, to be more precise - may convert it into a stationary variable. However, you should always keep in mind that the 'differenced' variable is a different economic variable from the plain variable. Therefore your model estimates should be described accordingly. Example: if log(employment) is non-stationary and you use log(employment)t - log(employment)t-1, instead, then the new variable is not employment, but the rate of growth of employment. I believe this answers whether you should use the exogenous variables in levels or first differences.
3. Stationarity: If the (initially) non-stationary variables are exogenous, then you have no choice than to use first differences or a another method (e.g. removing structural breaks) to make them stationary. If both of the endogenous variables are non-stationary, then either use first differences in both, or estimate your VAR in a VECM and 'pray' for cointegration. If only one of them is non-stationary, then again, you should 'transform' it into stationary or your VAR estimates would be, by definition, meaningless.
4. Endogeneity: Make sure that your exogenous variables are, indeed, exogenous. If one (ore more) are endogenous, then you should estimate the VAR as such. (i.e. with more than 2 equations). A standard exogeneity test includes Granger non-causality tests in 'auxiliary' VAR models.
Dear Pandelis,
The main reason why we use log values of variables is that most of the conomic variables are linear in their logarithmec values! Thus, to employ linear methods, we do this!
Mustafa Özer Dear, you mean that economic equations, not variables, are linear in their log transformation :).
Yes, e.g. Cobb-Douglas (a non-linear function) becomes linear in logs.
This is an additional reason, not the only one.
Thank you, for giving the chance to explain it a bit further.
Dear Mustafa Özer
There is no such thing as 'a linear variable'.
There is 'linear variable transformation', but that's a different story.
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