I am using VEC model and the out come variable and 'independent" variables are stationary at different forms. Specifically, the outcome variable is stationary in the log form but other variables are at their first difference. Can I use Log Linear relationship in estimating VEC please? If not what you suggest me?
I do like the solution of just adding a constant value to the series at hand, because it is a neat tranformation of a real variable. Another solution is just the log-transformation: any positive real variable x (not so small) can easily be transformed into y=log(x) and then, if the application is as simple as a regression, the coefficient is actually called an 'elasticity'. If x is a Price, then the x can easily be expressed in terms of cents instead of in terms of dollars OR the good for which x is paid can be redefined from kilos to tons, thus there will not be any problem with the asymptote (because x, the price, cannot be "small" enough). Provided that those pre-transformations are made (in physics you can also transform any measure into another), my solution is : y=log(x) if x>0 AND y= - log( - x) if x
First, note that a vector error correction (VEC) model is a restricted VAR designed for use with nonstationary series that are known to be cointegrated. The first ting to do therefore is to ensure that your series are not stationary at level but are cointegrated. I will suggest that you test for stationarity and the order of integration of the outcome variable (not in log form) to see if it is integrated of the same order with the other variables and then test for their cointegration and continue with your VEC on the unlogged if they are cointegrated.
If however the outcome variable is still stationry at level even when not logged or your objectives implies that it must be used in the log form that is I[0], whereas others are I[1], you have to resort to ARDL approach. See http://davegiles.blogspot.com.ng/2013/06/ardl-models-part-ii-bounds-tests.html for details on the approach.
Dear Carlos, thank you for the brief explanation. But i have still question in my mind. E. G. One of the variables is inflation and has positive and negative values, how can i transform to log, as some of the values are postive and some are negative. Can i use add some constant value method on this? Won't it be against the original meaning of the variable (e.g. all wz postive values if i add the maximum negative value as a constant)· waiting to hear from you. Thanks
I can only reemphasize the arguments of Nathaniel: a VEC require some form of nonstationarity, otherwise it woull collapse into a VAR model. In non-technical terms: you will only be able to capture joint long-term trend if your endogenous variables are not purely stationary. Concerning the transformation of individual variables in order to get the transformed results I(o) you are free to feed in anything: however the interpretation of your co-integration equation will be more complicated if some of its variables are in fact complex transformations of the original variables and you should be aware of changes in the distributions of underlying residuals: your goal are normally distributed residuals in both parts the co-integration part and the short-term adjustment part.
Hi Salomon, my pleasure. The meaning of the variable will not be lost because you can always convert the logs back to the initial levels (my previous solution allows you to get back to the levels). However, there are some provisos you have to consider. I strongly suggest to review Professor Lutkepohl's recent pieces of work: (1) Helmut Lütkepohl & Fang Xu (2011) Forecasting annual inflation with seasonal monthly data: Using levels versus logs of the underlying price index, Journal of Time Series Econometrics, 3(1), pgs. 1-23.
(2) Helmut Lütkepohl and Fang Xu (2012) The role of the log transformation in forecasting economic variables, Empirical Economics, 42(3), pgs. 619–638.
I have 6 variables and they are all l(1), my intention is to test for granger causality and then impulse response function; now my question is, is it appropriate to test for causality with the differenced data or with the original data? I read that the raw data should be used for causality test and then differenced/transformed data for the IRF and I also read elsewhere that stated the vice versa as appropriate...hence the confusion, can someone clarify this................................................
.And also, I know that when there is causality in one or both directions, there must be cointegration hence VECM, how can this vecm be simplified/refined ??? I can refine a VAR but cant seem to find how to do this to a VECM
Derbiw, if you are using stats write "help vec " in the command box, there is brief note wz examples regarding vec and post estimation after vec.
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