Monte Carlo Maximum Likelihood Estimation for Discretely Observed Diffusion Processes

By Alexandros Beskos, Omiros Papaspiliopoulos, Gareth O. Roberts. 2009

84 citations recorded by the source corpus.

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.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3d71d33dca44701497a1f12dd239ad639856de24

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Citations in the corpus

Bayesian inference for irreducible diffusion processes using the pseudo-marginal approach (2011, methodology): “A different approach for reducible diffusions, built upon exact simulation, has been developed in Beskos et al. (2006, 2009).”
Maximum-likelihood estimation for diffusion processes via closed-form density expansions (2013, methodology): “In particular, among various numerical methods, Lo [46] proposed to employ a numerical solution of Kolmogorov equation for transition density; Pedersen [55], Brandt and SantaClara [21], Durham and Gallant [25], Stramer and Yan [60], Beskos and Roberts [17], Beskos et al. [16], Beskos, Papaspiliopoul”
Particle filters for partially observed diffusions (2007, methodology): “Each path is a diffusion bridge starting from x (j) i−1|i and finishing at x (j) i and it can be simulated using EA, as described in Beskos et al. (2006a) and Beskos et al.”