Bias in the estimation of the mean reversion parameter in continuous time models

By Jun Yu. 2012

83 citations recorded by the source corpus.

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 obtain 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 when discretely sampled data are available. The first expression mimics the bias formula of Marriott and Pope (1954) for the discrete time model. 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 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.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/eed479bb0655405edff76eeb6dc0e16090439d58

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Citations in the corpus

Sample Size Recommendations for Continuous-Time Models: Compensating Shorter Time Series with Larger Numbers of Persons and Vice Versa (2020, result): “This is in line with a finding by Yu (2012) that bias is much more pronounced in continuous-time models than in their discrete-time counterparts.”
Folklore Theorems, Implicit Maps, and Indirect Inference (2012, background): “All of this research has a bearing on the estimation of continuous time models from discrete data, where similar problems of estimation bias for the mean reversion parameter arise but can be more severe (Tang and Chen, 2009; Yu, 2009).”