Monte Carlo maximum likelihood estimation for discretely observed diffusion processes

Details Monte Carlo maximum likelihood estimation for discretely observed diffusion processes Monte Carlo maximum likelihood estimation for discretely observed diffusion processes

2009-03-02

arxiv.org/abs/0903.0290v1

Annals of Statistics 2009, Vol. 37, No. 1, 223-245

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-AOS550 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

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 $n\to\infty$, 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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