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Optimal Jackknife for Discrete Time and Continuous Time Unit Root Models

Author

Listed:
  • Ye Chen

    (School of Economics, Singapore Management Unversity)

  • Jun Yu

    (School of Economics, Singapore Management Unversity)

Abstract

Maximum likelihood estimation of the persistence parameter in the discrete time unit root model is known for suffering from a downward bias. The bias is more pronounced in the continuous time unit root model. Recently Chambers and Kyriacou (2010) introduced a new jackknife method to remove the fi rst order bias in the estimator of the persistence parameter in a discrete time unit root model. This paper proposes an improved jackknife estimator of the persistence parameter that works for both the discrete time unit root model and the continuous time unit root model. The proposed jackknife estimator is optimal in the sense that it minimizes the variance. Simulations highlight the performance of the proposed method in both contexts. They show that our optimal jackknife reduces the variance of the jackknife method of Chambers and Kyriacou by at least 10% in both cases.

Suggested Citation

  • Ye Chen & Jun Yu, 2011. "Optimal Jackknife for Discrete Time and Continuous Time Unit Root Models," Working Papers 12-2011, Singapore Management University, School of Economics.
    • Handle: RePEc:siu:wpaper:12-2011
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    References listed on IDEAS

    as
    1. Tang, Cheng Yong & Chen, Song Xi, 2009. "Parameter estimation and bias correction for diffusion processes," Journal of Econometrics, Elsevier, vol. 149(1), pages 65-81, April.
    2. 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.
    3. Qiankun Zhou & Jun Yu, 2010. "Asymptotic Distributions of the Least Squares Estimator for Diffusion Processes," Working Papers 20-2010, Singapore Management University, School of Economics.
    4. Chiquoine, Benjamin & Hjalmarsson, Erik, 2009. "Jackknifing stock return predictions," Journal of Empirical Finance, Elsevier, vol. 16(5), pages 793-803, December.
    5. Peter C. B. Phillips, 2005. "Jackknifing Bond Option Prices," The Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 707-742.
    6. Jinyong Hahn & Whitney Newey, 2004. "Jackknife and Analytical Bias Reduction for Nonlinear Panel Models," Econometrica, Econometric Society, vol. 72(4), pages 1295-1319, July.
    7. Chambers, Marcus J., 2013. "Jackknife estimation of stationary autoregressive models," Journal of Econometrics, Elsevier, vol. 172(1), pages 142-157.
    8. 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.
    9. 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.
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    Citations

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    Cited by:

    1. Kyriacou, Maria, 2014. "Overlapping sub-sampling and invariance to initial conditions," Discussion Paper Series In Economics And Econometrics 1203, Economics Division, School of Social Sciences, University of Southampton.

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    More about this item

    Keywords

    Bias reduction; Variance reduction; Vasicek model; Long-span Asymptotics; Autoregression;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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