Published in Journal of Econometrics, 2011, https://doi.org/10.1016/j.jeconom.2010.12.006</p

Aït-Sahalia

Bergstrom

Black

Chan

Duffie

Durham

Feller

Florens-Zmirou

Fuller

Hannan

Hansen

Jun Yu

Milstein

Nicholls

Nowman

Pedersen

Peter C.B. Phillips

Phillips

Piazzesi

Sargan

Sundaresan

Tang

Vasicek

Xiaohu Wang

Yamamoto

English

Peter C. B. Phillips

Crossref

SSRN Electronic Journal

Bias in Estimating Multivariate and Univariate Diffusions

WANG, Xiaohu

PHILLIPS, Peter C. B.

YU, Jun

Institutional Knowledge at Singapore Management University

Journal of Econometrics

Bias in estimating multivariate and univariate diffusions

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

Wang, Xiaohu

Phillips, Peter C.B.

Yu, Jun

Yale University

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.208.394

Bias in Estimating Multivariate and Univariate Diffusions

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Institutional Knowledge at Singapore Management University

Crossref

Yale University

Institutional Knowledge at Singapore Management University