I would like to ask a question about error correction terms from VECM if I may. I am currently working on a lot of time-series data and one of the questions I would like to address is whether there is some relationship between different time-series. Reading around the subject it seemed to me that testing for cointegration would be a good way of showing that two or more time-series were in a long run equilibrium. However, before embarking on such procedures I wanted to be clear on a number of things.
Firstly, (assuming there is a cointegrating vector) I have been trying to work out how to interpret the error correction terms from a VECM. I have been using the vars package in R, which provides the error correction terms in the summary table for a vecm model. Now, as I understand it the error correction terms describe how the time-series adjust to disequilibrium.
I was wondering what the best way to interpret negative and positive error correction terms was?
Given two time-series Xt and Yt, from what I have read so far it seems that negative error correction terms would mean that when Yt-1 is above its long-run level then ΔY*t* will be negative, pulling Y back towards its long-run relationship with X.
On the other hand, I am less sure on the interpretation of a positive error correction term and I haven't been able to find a simple description.
Finally, I have been trying to discover how one could interpret ECTs when two or more cointegrating vectors exist. So far, the only thing I have found in the papers I have searched is that its very difficult.
Thank you for help, any advice, clarification etc. would be much appreciated.