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Jackknife estimation with a unit root

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  • Chambers, Marcus J.
  • Kyriacou, Maria

Abstract

We study jackknife estimators in a first-order autoregression with a unit root. Non-overlapping sub-sample estimators have different limit distributions, so the jackknife does not fully eliminate first-order bias. We therefore derive explicit limit distributions of the numerator and denominator to calculate the expectations that determine optimal jackknife weights. Simulations show that the resulting jackknife estimator produces substantial reductions in bias and RMSE.

Suggested Citation

  • Chambers, Marcus J. & Kyriacou, Maria, 2013. "Jackknife estimation with a unit root," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1677-1682.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:7:p:1677-1682
    DOI: 10.1016/j.spl.2013.03.016
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    References listed on IDEAS

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    1. Chambers, Marcus J., 2013. "Jackknife estimation of stationary autoregressive models," Journal of Econometrics, Elsevier, vol. 172(1), pages 142-157.
    2. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    3. Peter C. B. Phillips, 2005. "Jackknifing Bond Option Prices," The Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 707-742.
    4. Chambers, MJ & Kyriacou, M, 2010. "Jackknife Bias Reduction in the Presence of a Unit Root," Economics Discussion Papers 2785, University of Essex, Department of Economics.
    5. Rolf Larsson, 1998. "Bartlett Corrections for Unit Root Test Statistics," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(4), pages 425-438, July.
    6. Bravo, Francesco, 1999. "A Correction Factor For Unit Root Test Statistics," Econometric Theory, Cambridge University Press, vol. 15(2), pages 218-227, April.
    7. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    8. 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.
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    Cited by:

    1. Kruse, Yves Robinson & Kaufmann, Hendrik, 2015. "Bias-corrected estimation in mildly explosive autoregressions," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112897, Verein für Socialpolitik / German Economic Association.
    2. Kruse, Robinson & Kaufmann, Hendrik & Wegener, Christoph, 2018. "Bias-corrected estimation for speculative bubbles in stock prices," Economic Modelling, Elsevier, vol. 73(C), pages 354-364.
    3. Marcus J. Chambers & Maria Kyriacou, 2018. "Jackknife Bias Reduction in the Presence of a Near-Unit Root," Econometrics, MDPI, vol. 6(1), pages 1-28, March.
    4. Marcus J. Chambers, 2015. "A Jackknife Correction to a Test for Cointegration Rank," Econometrics, MDPI, vol. 3(2), pages 1-21, May.
    5. Chen, Ye & Yu, Jun, 2015. "Optimal jackknife for unit root models," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 135-142.
    6. Chambers, MJ & McCrorie, JR & Thornton, MA, 2017. "Continuous Time Modelling Based on an Exact Discrete Time Representation," Economics Discussion Papers 20497, University of Essex, Department of Economics.

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