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I have used the Johansen multivariate cointegration test to see whether a group of ten stock markets are cointegrated. However, I was wondering whether it would be possible to use the Gregory-Hansen and Enders-Siklos tests for structural-breaks and threshold adjustment on the entire system or whether they can only be used in a pairwise manner?

Any help is appreciated.

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The Gregory-Hansen and the Enders-Siklos tests are both residual based test. The formal theory of Philips and Ouliaris (1990) showed that for the linear cointegration test, critical values depend on the number of regressors. For the two non-linear versions you are interested in:

  • Gregory-Hansen: their formal derivations show that the statistic depends also on the number of regressors. They provide critical values, but only up to 4 regressors

  • Enders-Siklos: they do not provide a formal theory, and the critical values are derived from a DGP with 1 regressor.

So in both cases, you will have difficulties using these tests with 10 regressors. What you could do is to replicate the authors Monte Carlo simulations, and derive yourself the critical values for 10 regressors. Or maybe you will find more recent work allowing for more regressors (look maybe at Kejriwal and Perron for structural breaks?).

As an aside, note that residual-based tests apply when you have multiple variables but one single cointegrating relationship. Is this what you find in your data?

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