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On the non-existence of a Bartlett correction for unit root tests


  • Jensen, J. L.
  • Wood, Andrew T. A.


There has been considerable recent interest in testing for a unit root in autoregressive models, especially in the context of cointegration models in econometrics. The likelihood ratio test for a unit root has non-standard asymptotic behaviour. In particular, when the errors are Gaussian, the limiting null distribution of the likelihood ratio statistic, W, is a certain functional of Brownian motion, rather than chi-squared. Moreover, numerical work has shown that the limiting distribution of W is not always a good approximation to the actual distribution. Consequently, there is a need for improved distributional approximations, and the question of whether W admits a Bartlett correction is of interest. In this note we establish that a Bartlett correction does not exist in the simplest unit root model.

Suggested Citation

  • Jensen, J. L. & Wood, Andrew T. A., 1997. "On the non-existence of a Bartlett correction for unit root tests," Statistics & Probability Letters, Elsevier, vol. 35(2), pages 181-187, September.
  • Handle: RePEc:eee:stapro:v:35:y:1997:i:2:p:181-187

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    References listed on IDEAS

    1. Johansen, Soren & Juselius, Katarina, 1990. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 52(2), pages 169-210, May.
    2. Knight, J.L. & Satchell, S.E., 1993. "Asymptotic Expansions for Random Walks with Normal Errors," Econometric Theory, Cambridge University Press, vol. 9(03), pages 363-376, June.
    3. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, June.
    4. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
    5. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
    6. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    7. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
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    Cited by:

    1. Omtzigt Pieter & Fachin Stefano, 2002. "Bootstrapping and Bartlett corrections in the cointegrated VAR model," Economics and Quantitative Methods qf0212, Department of Economics, University of Insubria.
    2. Noud P.A. Giersbergen, 2013. "Bartlett correction in the stable second-order autoregressive model with intercept and trend," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(4), pages 482-498, November.
    3. Chambers, Marcus J. & Kyriacou, Maria, 2013. "Jackknife estimation with a unit root," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1677-1682.
    4. Alexei Onatski & Chen Wang, 2016. "Alternative Asymptotics for Cointegration Tests in Large VARs," Cambridge Working Papers in Economics 1637, Faculty of Economics, University of Cambridge.


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