Publication Type
Working Paper
Version
publishedVersion
Publication Date
10-2010
Abstract
Multivariate continuous time models are now widely used in economics and finance. Empirical applications typically rely on some process of discretization so that the system may be estimated with discrete data. This paper introduces a framework for discretizing linear multivariate continuous time systems that includes the commonly used Euler and trapezoidal approximations as special cases and leads to a general class of estimators for the mean reversion matrix. Asymptotic distributions and bias formulae are obtained for estimates of the mean reversion parameter. Explicit expressions are given for the discretization bias and its relationship to estimation bias in both multivariate and in univariate settings. In the univariate context, we compare the performance of the two approximation methods relative to exact maximum likelihood (ML) in terms of bias and variance for the Vasicek process. The bias and the variance of the Euler method are found to be smaller than the trapezoidal method, which are in turn smaller than those of exact ML. Simulations suggest that for plausible parameter settings the approximation methods work better than ML, the bias formulae are accurate, and for scalar models the estimates obtained from the two approximate methods have smaller bias and variance than exact ML. For the square root process, the Euler method outperforms the Nowman method in terms of both bias and variance. Simulation evidence indicates that the Euler method has smaller bias and variance than exact ML, Nowman’s method and the Milstein method.
Keywords
OLS, Continuous Time, Bias Reduction, Di¤usion, Euler approximation, Mil-stein approximation, Multivariate, Vasicek model.
Discipline
Econometrics
Research Areas
Econometrics
Volume
16-2010
First Page
1
Last Page
36
Publisher
SMU Economics and Statistics Working Paper Series, No. 16-2010
City or Country
Singapore
Citation
WANG, Xiaohu; PHILLIPS, Peter C. B.; and YU, Jun.
Bias in Estimating Multivariate and Univariate Diffusions. (2010). 16-2010, 1-36.
Available at: https://ink.library.smu.edu.sg/soe_research/1235
Copyright Owner and License
Authors
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Comments
Published in Journal of Econometrics, 2011, https://doi.org/10.1016/j.jeconom.2010.12.006