Open Access
February 2009 Monte Carlo maximum likelihood estimation for discretely observed diffusion processes
Alexandros Beskos, Omiros Papaspiliopoulos, Gareth Roberts
Ann. Statist. 37(1): 223-245 (February 2009). DOI: 10.1214/07-AOS550


This paper introduces a Monte Carlo method for maximum likelihood inference in the context of discretely observed diffusion processes. The method gives unbiased and a.s. continuous estimators of the likelihood function for a family of diffusion models and its performance in numerical examples is computationally efficient. It uses a recently developed technique for the exact simulation of diffusions, and involves no discretization error. We show that, under regularity conditions, the Monte Carlo MLE converges a.s. to the true MLE. For datasize n→∞, we show that the number of Monte Carlo iterations should be tuned as $\mathcal{O}(n^{1/2})$ and we demonstrate the consistency properties of the Monte Carlo MLE as an estimator of the true parameter value.


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Alexandros Beskos. Omiros Papaspiliopoulos. Gareth Roberts. "Monte Carlo maximum likelihood estimation for discretely observed diffusion processes." Ann. Statist. 37 (1) 223 - 245, February 2009.


Published: February 2009
First available in Project Euclid: 16 January 2009

zbMATH: 1169.65004
MathSciNet: MR2488350
Digital Object Identifier: 10.1214/07-AOS550

Primary: 65C30
Secondary: 62M05

Keywords: coupling , exact simulation , linear diffusion processes , random function , SLLN on Banach space , Uniform convergence

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 1 • February 2009
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