A quasi-maximum likelihood method for estimating the parameters of multivariate diffusions
AbstractThis paper develops a quasi-maximum likelihood (QML) procedure for estimating the parameters 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 diffusion 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.
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Bibliographic InfoPaper provided by National Centre for Econometric Research in its series NCER Working Paper Series with number 65.
Length: 35 pages
Date of creation: 28 Oct 2010
Date of revision:
stochastic differential equations; parameter estimation; quasi-maximum likelihood; moments;
Other versions of this item:
- Hurn, A.S. & Lindsay, K.A. & McClelland, A.J., 2013. "A quasi-maximum likelihood method for estimating the parameters of multivariate diffusions," Journal of Econometrics, Elsevier, vol. 172(1), pages 106-126.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-11-20 (All new papers)
- NEP-ECM-2010-11-20 (Econometrics)
- NEP-ORE-2010-11-20 (Operations Research)
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