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

Beskos, A., Dureau, J. and Kalogeropoulos, K. (2015) Bayesian inference for partially observed stochastic differential equations driven by fractional Brownian motion. Biometrika, 102 (4). pp. 809-827. ISSN 0006-3444

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Identification Number: 10.1093/biomet/asv051

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.

Item Type: Article
Official URL: http://biomet.oxfordjournals.org/
Additional Information: © 2015 Biometrika Trust
Divisions: Statistics
Subjects: Q Science > QA Mathematics
Sets: Departments > Statistics
Date Deposited: 04 Jan 2016 15:46
Last Modified: 20 Feb 2019 11:27
Projects: EP/K001264/1
Funders: Engineering and Physical Sciences Research Council
URI: http://eprints.lse.ac.uk/id/eprint/64806

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