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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Yong Bao & Aman Ullah & Yun Wang & Jun Yu, 2013. "Bias in the Mean Reversion Estimator in Continuous-Time Gaussian and Levy Processes," Working Papers CoFie-01-2013, Singapore Management University, Sim Kee Boon Institute for Financial Economics.
    • Handle: RePEc:skb:wpaper:cofie-03-2013
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    Cited by:

    1. Iglesias, Emma M., 2014. "Testing of the mean reversion parameter in continuous time models," Economics Letters, Elsevier, vol. 122(2), pages 187-189.
    2. Bao, Yong & Ullah, Aman & Wang, Yun & Yu, Jun, 2015. "Bias in the estimation of mean reversion in continuous-time Lévy processes," Economics Letters, Elsevier, vol. 134(C), pages 16-19.

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    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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