Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|improve this question
and if ECT is non significant but negative should i interpreted – user73706 Apr 26 '15 at 18:31
up vote 2 down vote accepted

After much researching I the following reference was the most useful to me when trying to interpret the findings of a vecm:

Helmut Lütkepohl, Markus Krätzig

Structural Vector Autoregressive Modeling and Impulse Responses pp. 159-196. In: Applied time-series economics.

A link to the chapter is given below:

share|improve this answer

ECT is consider good if the range between 0 ~ 1 but not more than 2. ECT should be in negative number and if positive value means explosive and not reasonable. For example, if the ECT(-1) estimated coefficient is -0.87 (The estimated coefficient indicates that about 87 per cent of this disequilibrium is corrected between 1 year (if annually data)). But if the ECT(-1) are -1.07 as an example (The estimated coefficient indicates that about 107 per cent of this disequilibrium is corrected between 1 year - and this does not make sense).

share|improve this answer
(The estimated coefficient indicates that about 107 per cent of this disequilibrium is corrected between 1 year - and this does not make sense). I think it is a theoretical question. It can make sense if we interpret it as "equilibrium is restored in less than one year". although, one might raise questions about the shock absorption/adjustment and flexibility of the economy. – user93356 Oct 27 '15 at 22:17

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.