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Test for the null hypothesis of cointegration with reduced size distortion


  • Eiji Kurozumi
  • Yoichi Arai


This paper considers a single equation cointegrating model and proposes the locally best invariant and unbiased (LBIU) test for the null hypothesis of cointegration. We derive the asymptotic local power functions and compare them with the standard residualbased test, and we show that the LBIU test is more powerful in a wide range of local alternatives. Then, we conduct a Monte Carlo simulation to investigate the nite sample properties of the tests and show that the LBIU test outperforms the residual-based test in terms of both size and power. The advantage of the LBIU test is particularly patent when the error is highly autocorrelated. Further, we point out that nite sample performance of existing tests is largely affected by the initial value condition while our tests are immune to it. We propose a simple transformation of data that resolves the problem in the existing tests.

Suggested Citation

  • Eiji Kurozumi & Yoichi Arai, 2006. "Test for the null hypothesis of cointegration with reduced size distortion," Hi-Stat Discussion Paper Series d06-190, Institute of Economic Research, Hitotsubashi University.
  • Handle: RePEc:hst:hstdps:d06-190

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    References listed on IDEAS

    1. Christian Dustmann & Costas Meghir, 2005. "Wages, Experience and Seniority," Review of Economic Studies, Oxford University Press, vol. 72(1), pages 77-108.
    2. Olley, G Steven & Pakes, Ariel, 1996. "The Dynamics of Productivity in the Telecommunications Equipment Industry," Econometrica, Econometric Society, vol. 64(6), pages 1263-1297, November.
    3. Dostie, Benoit, 2005. "Job Turnover and the Returns to Seniority," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 192-199, April.
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    Cited by:

    1. Hadri, Kaddour & Kurozumi, Eiji & Rao, Yao, 2013. "Novel Panel Cointegration Tests Emending for Cross-Section Dependence with N Fixed," Discussion Papers 2013-12, Graduate School of Economics, Hitotsubashi University.

    More about this item


    Cointegration; locally best test; point optimal test;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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