Limit Theory for Multivariate Linear Diffusion Estimation

Abstract

Multivariate linear diffusions have been widely used in economics and finance. Most of the research rely on different kinds of approximate discrete time model to do estimation, which makes the estimate suffer from specification error and not be consistent once time interval is fixed. One major reason of using approximate discrete models is that the maximum likelihood (ML) estimate based on exact discrete model requires the calculation of matrix logarithm which is difficult to do. Facilitated by a new representation of principal logarithm in linear algebra literature, the paper proposes a new ML estimator starting from exact discrete time model. The new estimator enjoys three major advantages comparing with the traditional one. Both theoretical analysis and simulation results are given to illustrate it. The consistency and asymptotic distribution are derived in the cases where the model is stationary, pure unit roots, or partially nonstationary. Special attention is paid on getting explicit expressions for the asymptotic covariance matrix, especially in low dimensional cases. An empirical application is conducted on daily realized volatility data on Pound, Euro and Yen exchange rates, illustrating the implementation of the theory. Although the theory is derived for linear diffusions, all results can be extended straightforwardly to diffusions with nonlinear diffusion term when Norman approximation is used to estimate.

Presenter:

Xiaohu Wang (PhD Candidate)
Singapore Management University

Date:

Friday, 19 October 2012

Time:

3:45pm - 5.15pm

Venue:

Seminar Room 5.1, Level 5
School of Economics
Singapore Management University
90 Stamford Road
Singapore 178903

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Registration:

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