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

Jun Yu

Working Papers from Singapore Management University, Sim Kee Boon Institute for Financial Economics

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.

Keywords: Least squares; Maximum likelihood; Discrete sampling; Continuous record; Near unit root (search for similar items in EconPapers)
JEL-codes: C22 C32 (search for similar items in EconPapers)
Pages: 27 Pages
Date: 2007-04, Revised 2008-10
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Published in SMU-SKBI CoFie Working Paper

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http://www.smu.edu.sg/institutes/skbife/downloads/ ... %20Time%20Models.pdf

Related works:
Journal Article: Bias in the estimation of the mean reversion parameter in continuous time models (2012)
Working Paper: Bias in the Estimation of the Mean Reversion Parameter in Continuous Time Models (2009)
Working Paper: Bias in the Estimation of the Mean Reversion Parameter in Continuous Time Models (2009)
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