A Quasi-Maximum Likelihood Method for Estimating the Parameters of Multivariate Diffusions
Stan Hurn1, Kenneth Lindsay2, Andrew McClelland1
1School of Economics and Finance, Queensland University of Technology, Brisbane, Australia; 2Dept. of Mathematics, University of Glasgow, United Kingdom

This paper develops a quasi-maximum likelihood (QML) procedure for estimating the parame- ters of multi-dimensional stochastic differential equations. The transitional density is taken to be a time-varying multivariate Gaussian where the first two moments of the distribution are approximately the true moments of the unknown transitional density. For affine drift and diffu- sion functions, the moments are shown to be exactly those of the true transitional density and for nonlinear drift and diffusion functions the approximation is extremely good. The estimation procedure is easily generalizable to models with latent factors, such as the stochastic volatility class of model. The QML method is as effective as alternative methods when proxy variables are used for unobserved states. A conditioning estimation procedure is also developed that allows parameter estimation in the absence of proxies.

Keywords: Stochastic differential equations; Parameter estimation; Quasi maximum likelihood; Moments

Biography: Stan Hurn graduated with a D.Phil. in Economics from (St. Edmund Hall) Oxford in 1992. He worked as a lecturer in the Department of Political Economy at the University of Glasgow from 1988 to 1995 and was appointed Official Fellow in Economics at Brasenose College, Oxford in 1996. In 1998 he joined the Queensland University of Technology as a Professor of Econometrics in the School of Economics and Finance.