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Optimal jackknife for unit root models

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  • Chen, Ye
  • Yu, Jun

Abstract

A new jackknife method is introduced to remove the first order bias in unit root models. It is optimal in the sense that it minimizes the variance among all the jackknife estimators of the form considered in Phillips and Yu (2005) and Chambers and Kyriacou (2013) after the number of subsamples is selected. Simulations show that the new jackknife reduces the variance of that of Chambers and Kyriacou by about 10% for any selected number of subsamples without compromising bias reduction. The results continue to hold true in near unit root models.

Suggested Citation

  • Chen, Ye & Yu, Jun, 2015. "Optimal jackknife for unit root models," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 135-142.
    • Handle: RePEc:eee:stapro:v:99:y:2015:i:c:p:135-142
    DOI: 10.1016/j.spl.2014.12.014
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    References listed on IDEAS

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    1. Sargan, J D, 1976. "Econometric Estimators and the Edgeworth Approximation," Econometrica, Econometric Society, vol. 44(3), pages 421-448, May.
    2. Chambers, Marcus J., 2013. "Jackknife estimation of stationary autoregressive models," Journal of Econometrics, Elsevier, vol. 172(1), pages 142-157.
    3. repec:adr:anecst:y:1986:i:4:p:05 is not listed on IDEAS
    4. Peter C. B. Phillips, 2005. "Jackknifing Bond Option Prices," The Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 707-742.
    5. Yu, Jun, 2012. "Bias in the estimation of the mean reversion parameter in continuous time models," Journal of Econometrics, Elsevier, vol. 169(1), pages 114-122.
    6. Jan R. Magnus, 1986. "The Exact Moments of a Ratio of Quadratic Forms in Normal Variables," Annals of Economics and Statistics, GENES, issue 4, pages 95-109.
    7. Bao, Yong & Ullah, Aman & Zinde-Walsh, Victoria, 2013. "On existence of moment of mean reversion estimator in linear diffusion models," Economics Letters, Elsevier, vol. 120(2), pages 146-148.
    8. Chambers, Marcus J. & Kyriacou, Maria, 2013. "Jackknife estimation with a unit root," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1677-1682.
    9. Phillips, Peter C.B. & Magdalinos, Tassos, 2009. "Unit Root And Cointegrating Limit Theory When Initialization Is In The Infinite Past," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1682-1715, December.
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    Cited by:

    1. Kanchana Nadarajah & Gael M Martin & Donald S Poskitt, 2019. "Optimal Bias Correction of the Log-periodogram Estimator of the Fractional Parameter: A Jackknife Approach," Monash Econometrics and Business Statistics Working Papers 7/19, Monash University, Department of Econometrics and Business Statistics.
    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. Xi Chen & Kyoung-Kuk Kim, 2016. "Efficient VaR and CVaR Measurement via Stochastic Kriging," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 629-644, November.

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