Publication Type
Journal Article
Version
acceptedVersion
Publication Date
4-2011
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 when the mean reversion is slow, 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
Bias, Diffusion, Euler approximation, Trapezoidal approximation, Milstein approximation
Discipline
Econometrics
Research Areas
Econometrics
Publication
Journal of Econometrics
Volume
161
Issue
2
First Page
228
Last Page
245
ISSN
0304-4076
Identifier
10.1016/j.jeconom.2010.12.006
Publisher
Elsevier
Citation
WANG, Xiaohu; PHILLIPS, Peter C. B.; and YU, Jun.
Bias in Estimating Multivariate and Univariate Diffusions. (2011). Journal of Econometrics. 161, (2), 228-245.
Available at: https://ink.library.smu.edu.sg/soe_research/1311
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.
Additional URL
https://doi.org/10.1016/j.jeconom.2010.12.006