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

This paper develops the approximate finite-sample bias of the ordinary least squares or quasi maximum likelihood estimator of the mean reversion parameter in continuous-time Lévy 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 difference scenarios. However, when the time span is small and the mean reversion parameter is approaching its lower bound, we find it more difficult to approximate well the finite-sample bias. JEL Classification: C10, C22 ∗Corresponding Author: Department of Economics, Purdue University, 403 W. State Street, West Lafayette, IN 47907. Email: [email protected]. †Department of Economics, University of California, Riverside, CA 92521. E-mail: [email protected]. ‡School of International Trade and Economics, University of International Business and Economics, Beijing, China. E-mail: [email protected]. §Sim Kee Boon Institute for Financial Economics, School of Economics and Lee Kong Chian School of Business, Singapore Management University, Singapore 178903. E-mail: [email protected]. 1