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Bayesian inference for partially observed stochastic differential equations driven by fractional Brownian motion

Beskos, A; Dureau, J; Kalogeropoulos, K; (2015) Bayesian inference for partially observed stochastic differential equations driven by fractional Brownian motion. Biometrika , 102 (4) pp. 809-827. 10.1093/biomet/asv051. Green open access

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Abstract

We consider continuous-time diffusion models driven by fractional Brownian motion. Observations are assumed to possess a nontrivial likelihood given the latent path. Due to the non-Markovian and high-dimensional nature of the latent path, estimating posterior expectations is computationally challenging. We present a reparameterization framework based on the Davies and Harte method for sampling stationary Gaussian processes and use it to construct a Markov chain Monte Carlo algorithm that allows computationally efficient Bayesian inference. The algorithm is based on a version of hybrid Monte Carlo simulation that delivers increased efficiency when used on the high-dimensional latent variables arising in this context. We specify the methodology on a stochastic volatility model, allowing for memory in the volatility increments through a fractional specification. The method is demonstrated on simulated data and on the S&P 500/VIX time series. In the latter case, the posterior distribution favours values of the Hurst parameter smaller than 1/2, pointing towards medium-range dependence.

Type: Article
Title: Bayesian inference for partially observed stochastic differential equations driven by fractional Brownian motion
Open access status: An open access version is available from UCL Discovery
DOI: 10.1093/biomet/asv051
Publisher version: http://dx.doi.org/10.1093/biomet/asv051
Language: English
Additional information: © 2015 Biometrika Trust. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/ licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
Keywords: Bayesian inference, Davies and Harte algorithm, Fractional Brownian motion, Hybrid Monte Carlo algorithm
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/1474799
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