Beskos, Alexandros, Papaspiliopoulos, Omiros and Roberts, Gareth O. (2009) Monte Carlo maximum likelihood estimation for discretely observed diffusion processes. Annals of statistics, Vol.37 (No.1). pp. 223-245. doi:10.1214/07-AOS550

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Abstract

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 aid 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 -> infinity, we show that the number of Monte Carlo iterations should be tuned as O (n(1/2)) and we demonstrate the consistency properties of the Monte Carlo MLE as an estimator of the true parameter value.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Journal or Publication Title:	Annals of statistics
Publisher:	Inst Mathematical Statistics
ISSN:	0090-5364
Official Date:	February 2009
Dates:	Date Event February 2009 Published
Volume:	Vol.37
Number:	No.1
Number of Pages:	23
Page Range:	pp. 223-245
DOI:	10.1214/07-AOS550
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Greek State Scholarship's Foundation, Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	GR/S61577/01 (EPSRC)

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