Computational Statistics

, Volume 28, Issue 6, pp 2719–2748 | Cite as

The power of bootstrap tests of cointegration rank

  • Niklas Ahlgren
  • Jan Antell
Original Paper


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.


Bootstrap Cointegration Euribor interest rates Likelihood ratio test Test power 



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.


  1. Ahlgren N, Antell J (2008) Bootstrap and fast double bootstrap tests of cointegration rank with financial time series. Comput Stat Data Anal 52:4754–4767Google Scholar
  2. Bollerslev T (1990) Modelling the coherence in short-run nominal exchange rates: a multivariate generalized ARCH model. Rev Econ Stat 72:498–505CrossRefGoogle Scholar
  3. Cavaliere G, Rahbek A, Taylor AMR (2012) Bootstrap determination of the co-integration rank in vector autoregressive models. Econometrica 80:1721–1740MathSciNetCrossRefzbMATHGoogle Scholar
  4. Davidson R, MacKinnon JG (2000) Bootstrap tests: how many bootstraps? Econom Rev 19:55–68MathSciNetCrossRefzbMATHGoogle Scholar
  5. Davidson R, MacKinnon JG (2006) The power of bootstrap and asymptotic tests. J Econom 133:421–441MathSciNetCrossRefGoogle Scholar
  6. Doornik JA (1998) Approximations to the asymptotic distribution of cointegration tests. J Econ Surv 12:573–593CrossRefGoogle Scholar
  7. Hall AD, Anderson HM, Granger CWJ (1992) A cointegration analysis of treasury bill yields. Rev Econ Stat 74:116–126CrossRefGoogle Scholar
  8. Johansen S (1996) Likelihood-based inference in cointegrated vector autoregressive models. Oxford University Press, OxfordGoogle Scholar
  9. Johansen S (2002) A small sample correction for the test of cointegrating rank in the vector autoregressive model. Econometrica 70:1929–1961MathSciNetCrossRefzbMATHGoogle Scholar
  10. Juselius K (2006) The cointegrated VAR model. Methodology and applications. Oxford University Press, OxfordzbMATHGoogle Scholar
  11. Saikkonen P, Lütkepohl H (1999) Local power of likelihood ratio tests for the cointegrating rank of a VAR process. Econom Theory 15:50–78Google Scholar
  12. Swensen AR (2006) Bootstrap algorithms for testing and determining the cointegration rank in VAR models. Econometrica 74:1699–1714MathSciNetCrossRefzbMATHGoogle Scholar
  13. Swensen AR (2009) Corrigendum to ’Bootstrap algorithms for testing and determining the cointegration rank in VAR models’. Econometrica 77:1703–1704MathSciNetCrossRefzbMATHGoogle Scholar
  14. van Giersbergen NPA (1996) Bootstrapping the trace statistic in VAR models: Monte Carlo results and applications. Oxf Bull Econ Stat 58:391–408CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Finance and Statistics, Hanken School of EconomicsHelsinkiFinland

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