# The power of bootstrap tests of cointegration rank

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## Abstract

Bootstrap likelihood ratio tests of cointegration rank are commonly used because they tend to have rejection probabilities that are closer to the nominal level than the rejection probabilities of asymptotic tests. The effect of bootstrapping the test on its power is largely unknown. We show that a new computationally inexpensive procedure can be applied to the estimation of the power function of the bootstrap test of cointegration rank. The bootstrap test is found to have a power function close to that of the level-adjusted asymptotic test. The bootstrap test therefore estimates the level-adjusted power of the asymptotic test highly accurately. The bootstrap test may have low power to reject the null hypothesis of cointegration rank zero, or underestimate the cointegration rank. An empirical application to Euribor interest rates is provided as an illustration of the findings.

## Keywords

Bootstrap Cointegration Euribor interest rates Likelihood ratio test Test power## Notes

### Acknowledgments

The authors want to thank two anonymous referees for their comments, and the Editor. Their comments have greatly improved the paper. The paper was presented in the 57th Session of the International Statistical Institute, Durban, 2009, and the 3rd International Conference on Computational and Financial Econometrics, 2009, Limassol. Niklas Ahlgren acknowledges financial support from Magnus Ehrnrooths Stiftelse.

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