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A Correction Factor For Unit Root Test Statistics

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  • Bravo, Francesco

Abstract

Despite the fact that it is not correct to speak of Bartlett corrections in the case of nonstationary time series, this paper shows that a Bartlett-type correction to the likelihood ratio test for a unit root can be an effective tool to control size distortions. Using well-known formulae, we obtain second-order (numerical) approximations to the moments and cumulants of the likelihood ratio, which makes it possible to calculate a Bartlett-type factor. It turns out that the cumulants of the corrected statistic are closer to their asymptotic value than the original one. A simulation study is then carried out to assess the quality of these approximations for the first four moments; the size and the power of the original and the corrected statistic are also simulated. Our results suggest that the proposed correction reduces the size distortion without affecting the power too much.

Suggested Citation

  • Bravo, Francesco, 1999. "A Correction Factor For Unit Root Test Statistics," Econometric Theory, Cambridge University Press, vol. 15(2), pages 218-227, April.
    • Handle: RePEc:cup:etheor:v:15:y:1999:i:02:p:218-227_15
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    Cited by:

    1. Noud P.A. van 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.
    2. Canepa Alessandra, 2022. "Small Sample Adjustment for Hypotheses Testing on Cointegrating Vectors," Journal of Time Series Econometrics, De Gruyter, vol. 14(1), pages 51-85, January.
    3. Canepa, Alessandra, 2020. "Improvement on the LR Test Statistic on the Cointegrating Relations in VAR Models: Bootstrap Methods and Applications," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202007, University of Turin.
    4. Chambers, Marcus J. & Kyriacou, Maria, 2013. "Jackknife estimation with a unit root," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1677-1682.
    5. Pere, Pekka, 2000. "Adjusted estimates and Wald statistics for the AR(1) model with constant," Journal of Econometrics, Elsevier, vol. 98(2), pages 335-363, October.

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