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Bias in the Estimation of the Mean Reversion Parameter in Continuous Time Models

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  • Jun Yu

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

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Abstract

It is well known that for continuous time models with a linear drift standard estimation methods yield biased estimators for the mean reversion parameter both in finite discrete samples and in large in-fill samples. In this paper, we derive two expressions to approximate the bias of the least squares/maximum likelihood estimator of the mean reversion parameter in the Ornstein-Uhlenbeck process with a known long run mean and with an unknown long run mean. The first expression mimics the bias formula of Marriott and Pope (1954) for the discrete time model and corresponds to the bias formula of Tang and Chen (2007). Simulations show that this expression does not work satisfactorily when the speed of mean reversion is slow. Slow mean reversion corresponds to the near unit root situation and is empirically realistic for many financial time series. An improvement is made in the second expression where a nonlinear correction term is included into the bias formula. It is shown that the nonlinear term is important in the near unit root situation. Simulations indicate that the second expression captures the magnitude, the curvature and the non-monotonicity of the actual bias better than the first expression.

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File URL: http://www.smu.edu.sg/institutes/skbife/downloads/CoFiE/Working%20Papers/Bias%20in%20the%20Estimation%20of%20the%20Mean%20Reversion%20Parameter%20in%20Continuous%20Time%20Models.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-06-2008.

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Length: 27 Pages
Date of creation: Apr 2007
Date of revision: Oct 2008
Publication status: Published in SMU-SKBI CoFie Working Paper
Handle: RePEc:skb:wpaper:cofie-06-2008

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Keywords: Least squares; Maximum likelihood; Discrete sampling; Continuous record; Near unit root;

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Citations

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Cited by:
  1. Wang, Xiaohu & Phillips, Peter C.B. & Yu, Jun, 2011. "Bias in estimating multivariate and univariate diffusions," Journal of Econometrics, Elsevier, vol. 161(2), pages 228-245, April.
  2. Iglesias, Emma M., 2014. "Testing of the mean reversion parameter in continuous time models," Economics Letters, Elsevier, vol. 122(2), pages 187-189.
  3. Daniel Andrei & Bruce Carlin & Michael Hasler, 2014. "Model Disagreement and Economic Outlook," NBER Working Papers 20190, National Bureau of Economic Research, Inc.
  4. 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.
  5. Peter C.B. Phillips & Jun Yu, 2007. "Simulation-based Estimation of Contingent-claims Prices," Cowles Foundation Discussion Papers 1596, Cowles Foundation for Research in Economics, Yale University.
  6. 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.
  7. Peter C. B. Phillips & Shu-Ping Shi & Jun Yu, 2013. "Testing for Multiple Bubbles 1: Historical Episodes of Exuberance and Collapse in the S&P 500," Working Papers CoFie-03-2013, Sim Kee Boon Institute for Financial Economics.
  8. Yong Bao & Aman Ullah & Yun Wang & Jun Yu, 2013. "Bias in the Mean Reversion Estimator in Continuous-Time Gaussian and Lévy Processes," Working Papers 02-2013, Singapore Management University, School of Economics.

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