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Monte Carlo Maximum Likelihood Estimation for Discretely Observed Diffusion Processes

Beskos, A; Papaspiliopoulos, O; Roberts, G; (2009) Monte Carlo Maximum Likelihood Estimation for Discretely Observed Diffusion Processes. The Annals of Statistics , 37 (1) 223 - 245. 10.1214/07-AOS550. Green open access

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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.

Type: Article
Title: Monte Carlo Maximum Likelihood Estimation for Discretely Observed Diffusion Processes
Open access status: An open access version is available from UCL Discovery
DOI: 10.1214/07-AOS550
Publisher version: http://dx.doi.org/10.1214/07-AOS550
Language: English
Additional information: This version is the version of record . For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Coupling, uniform convergence, exact simulation, linear diffusion processes, random function, SLLN on Banach space, EXACT SIMULATION, ERGODIC THEOREM, MODELS, INFERENCE, CONVERGENCE, TIME
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/140952
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