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Optimal Jackknife for Discrete Time and Continuous Time Unit Root Models

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  • Ye Chen

    ()
    (School of Economics, Singapore Management Unversity)

  • Jun Yu

    ()
    (School of Economics, Singapore Management Unversity)

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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.

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Bibliographic Info

Paper provided by Singapore Management University, School of Economics in its series Working Papers with number 12-2011.

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Length: 28 pages
Date of creation: Oct 2011
Date of revision:
Publication status: Published in SMU Economics and Statistics Working Paper Series
Handle: RePEc:siu:wpaper:12-2011

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Related research

Keywords: Bias reduction; Variance reduction; Vasicek model; Long-span Asymptotics; Autoregression;

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References

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  1. Benjamin Chiquoine & Erik Hjalmarsson, 2008. "Jackknifing stock return predictions," International Finance Discussion Papers 932, Board of Governors of the Federal Reserve System (U.S.).
  2. Peter C.B. Phillips & Jun Yu, 2003. "Jackknifing Bond Option Prices," Cowles Foundation Discussion Papers 1392, Cowles Foundation for Research in Economics, Yale University.
  3. Jinyong Hahn & Whitney Newey, 2004. "Jackknife and Analytical Bias Reduction for Nonlinear Panel Models," Econometrica, Econometric Society, vol. 72(4), pages 1295-1319, 07.
  4. 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.
  5. Jun Yu, 2007. "Bias in the Estimation of the Mean Reversion Parameter in Continuous Time Models," Working Papers CoFie-06-2008, Sim Kee Boon Institute for Financial Economics, revised Oct 2008.
  6. 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(06), pages 1682-1715, December.
  7. Marcus J Chambers & Maria Kyriacou, 2010. "Jackknife Bias Reduction in the Presence of a Unit Root," Economics Discussion Papers 685, University of Essex, Department of Economics.
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Cited by:
  1. Kyriacou, Maria, 2012. "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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