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

Beskos, A., Dureau, J. and Kalogeropoulos, K. ORCID: 0000-0002-0330-9105 (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 Oct 2021 02:18
Projects: EP/K001264/1
Funders: Engineering and Physical Sciences Research Council
URI: http://eprints.lse.ac.uk/id/eprint/64806

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