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December 2011 On the approximate maximum likelihood estimation for diffusion processes
Jinyuan Chang, Song Xi Chen
Ann. Statist. 39(6): 2820-2851 (December 2011). DOI: 10.1214/11-AOS922


The transition density of a diffusion process does not admit an explicit expression in general, which prevents the full maximum likelihood estimation (MLE) based on discretely observed sample paths. Aït-Sahalia [J. Finance 54 (1999) 1361–1395; Econometrica 70 (2002) 223–262] proposed asymptotic expansions to the transition densities of diffusion processes, which lead to an approximate maximum likelihood estimation (AMLE) for parameters. Built on Aït-Sahalia’s [Econometrica 70 (2002) 223–262; Ann. Statist. 36 (2008) 906–937] proposal and analysis on the AMLE, we establish the consistency and convergence rate of the AMLE, which reveal the roles played by the number of terms used in the asymptotic density expansions and the sampling interval between successive observations. We find conditions under which the AMLE has the same asymptotic distribution as that of the full MLE. A first order approximation to the Fisher information matrix is proposed.


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Jinyuan Chang. Song Xi Chen. "On the approximate maximum likelihood estimation for diffusion processes." Ann. Statist. 39 (6) 2820 - 2851, December 2011.


Published: December 2011
First available in Project Euclid: 24 January 2012

zbMATH: 1246.62181
MathSciNet: MR3012393
Digital Object Identifier: 10.1214/11-AOS922

Primary: 62M05
Secondary: 62F12

Keywords: asymptotic expansion , asymptotic normality , consistency , discrete time observation , maximum likelihood estimation

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.39 • No. 6 • December 2011
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