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

• 成果类型: Article
• 署名作者: Beskos, A.; Dureau, J.; Kalogeropoulos, K.
• 署名单位: University of London; University College London; University of London; London School Economics & Political Science
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asv051
• 发表日期: 2015
• 页码: 809827
• 关键词: hybrid monte-carlo; long-memory; mcmc methods; volatility; persistence

摘要

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.