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Bias in the Mean Reversion Estimator in Continuous-Time Gaussian and Levy Processes

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Author Info

  • Yong Bao

    (Purdue University)

  • Aman Ullah

    (University of California, Riverside)

  • Yun Wang

    (University of International Business and Economics)

  • Jun Yu

    (Sim Kee Boon Institute for Financial Economics, Singapore Management University)

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    Abstract

    This paper develops the approximate nite-sample bias of the ordinary least squares or quasi maximum likelihood estimator of the mean reversion parameter in continuous-time Levy processes. For the special case of Gaussian processes, our results reduce to those of Tang and Chen (2009) (when the long-run mean is unknown) and Yu (2012) (when the long-run mean is known). Simulations show that in general the approximate bias works well in capturing the true bias of the mean reversion estimator under di erence scenarios. However, when the time span is small and the mean reversion parameter is approaching its lower bound, we nd it more dicult to approximate well the nite-sample bias.

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    File URL: http://skbi.smu.edu.sg/sites/default/files/skbife/paper_no._cofie-wp-01-2013.pdf
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    Bibliographic Info

    Paper provided by Sim Kee Boon Institute for Financial Economics in its series Working Papers with number CoFie-01-2013.

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    Length: 20 Pages
    Date of creation: Feb 2013
    Date of revision:
    Publication status: Published in SMU-SKBI CoFie Working Paper
    Handle: RePEc:skb:wpaper:cofie-03-2013

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    Related research

    Keywords: Date-stamping strategy; Flexible window; Generalized sup ADF test; Multiple bubbles; Rational bubble; Periodically collapsing bubbles; Sup ADF test;

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    References

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    1. Jun Yu, 2009. "Bias in the Estimation of the Mean Reversion Parameter in Continuous Time Models," Working Papers, Singapore Management University, School of Economics 16-2009, Singapore Management University, School of Economics.
    2. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, Econometric Society, vol. 53(2), pages 385-407, March.
    3. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 12(04), pages 627-627, November.
    4. Ullah, Aman, 2004. "Finite Sample Econometrics," OUP Catalogue, Oxford University Press, Oxford University Press, edition 1, number 9780198774488, October.
    5. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, Elsevier, vol. 5(2), pages 177-188, November.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
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    Cited by:
    1. Etienne, Xiaoli L. & Irwin, Scott H. & Garcia, Philip, 2014. "Bubbles in food commodity markets: Four decades of evidence," Journal of International Money and Finance, Elsevier, Elsevier, vol. 42(C), pages 129-155.

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