I have some cointegrated series and I decided to build a VECM model.
(I differentiated them twice in order to get stationary series and that led me to believe that they might be cointegrated – I applied a cointegration test on the original series and they are cointegrated, so a VECM is recommended.)
I understand that VAR models are usually applied on stationary series, but that the VECM should consider the original series. Is that right? Could someone point me to a material where it is explained why this situation is like this?
Best Answer
Consider a number of I(1) processes that are cointegrated so that their linear combination is stationary. (Higher orders of integration and cointegration are straightforward to generalize to).
When testing for cointegration using the Johansen or the Engle-Granger tests, original series (rather than their first differences) are used.
The dependent variables of a VECM are the first differences. However, the software will normally require to input the original variables for estimating a VECM -- check the documentation carefully.
All of this can be found in any modern time series textbook (e.g. Lutkepohl "New Introduction to Multiple Time Series Analysis" (2005)) or e.g. here (there are more good online resources, just search for "vector error correction model").
Also note that in economic and financial applications it is normally enough to difference the data once to achieve stationarity. If the first differences of your data are nonstationary, perhaps your data is not only integrated of order one but also contain structural breaks or other "unpleasant" features. Differencing more than once need not be the best solution then.