Tuesday, June 28, 2011

p-Values for Cointegration Tests With Breaks in the Data

In an earlier post I went through some econometrics that involved the problem of testing for multivariate cointegration in the case where there are one or more trend-breaks or level-breaks in the time-series data.  Specifically, I talked about the modified Trace tests introduced by Johansen et al. (2000), and I mentioned the really nice discussion of the application of these tests that is provided by Joyeux (2007).

Two things relating to this occurred to me recently. The first was that while I'd provided EViews code for calculating asymptotic critical values to be used with these tests, it would also be useful to have the corresponding code for calculating p-values for any calculated values of the Trace test statistics.

Second, given the discussion and comments in my recent posts (here and here) about open-source software, I thought it would be a good idea to make the p-values and critical values code available for users of R. (Thanks for the earlier comments, "Ben" and Tal Galili!)

So, in a joint effort, Ryan Godwin and I have written the R code, and extended the earlier EViews code to compute the p-values. Both of them are on the Code  page that goes with this blog - in two places: under this post, and also in place of the code for the earlier post. (You can thank Ryan for the nice windows that open when you run the R program.) In addition, an Excel workbook with a big selection of critical values is avalable on the Data page for this blog.

We hope you find the programs useful!

Note: The links to the following references will be helpful only if your computer's IP address gives you access to the electronic versions of the publications in question. That's why a written References section is provided.


Johansen, S., R. Mosconi and B. Nielsen (2000). Cointegration analysis in the presence of structural breaks in the deterministic trend. Econometrics Journal, 3, 216-249.

Joyeux, R. (2007). How to deal with structural breaks in practical cointegration analysis? In B. B. Rao (ed.), Cointegration for the Applied Economist, Second Edition, Palgrave Macmillan, New York, 195-221.

© 2011, David E. Giles


  1. Al*R*ight, this is terrific! Many thanks!

  2. Thanks Ben - your earlier comments were much appreciated.

  3. dear prof DG
    I hope that all econometricians have read your good book , it has a good notes about P-value of co integration and fruitful information.
    thanks sir
    Dr. Mohammad Alaya
    jordan-Hussein university

  4. Mohammad: Thanks for the kind feedback.


  5. Dear Professor Giles

    Please can you tell me if cointegration tests are applicable to the estimated residuals for a regression through the origin OLS model? Are there published refereed articles on this topic?

    Thank you

    Mark Darroch

    1. Mark: Thanks for the question. I guess yo're referring to the Engle-Granger 2-step method of testing. In that case, the answer is "no". You need to include an intercept in the first-stage regression, and you may also include a linear trend. This choice affects the distribution of teh ADF test statistic at the second stage. That's why there are 2 sets of critical values - one for intercept-only at the first stage; and one for intercept and trend at he first stage.

      At the second stage, where you apply the ADF test to the first-stage residuals, this test MUST be applied using the no-drift/no-trend option, regardless of which choice yo made at stage 1.

      I hope this helps.


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