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

A. Beskos, J. Dureau, K. Kalogeropoulos
2015 Biometrika  
Original citation: 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. SUMMARY We consider continuous-time diffusion models driven by fractional Brownian motion. Observations are assumed to possess a non-trivial likelihood given the latent path. Due to the non-Markovianity and high dimensionality of the latent paths, estimating posterior expectations is
more » ... utationally 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 that delivers increased efficiency when applied 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 methodology is illustrated on simulated data and on the S&P500/VIX time series the posterior distribution favours values of the Hurst parameter, smaller than 1/2, pointing towards medium range dependence. Some key words: Bayesian inference; Davies and Harte algorithm; fractional Brownian motion; hybrid Monte Carlo. arXiv:1307.0238v5 [stat.ME]
doi:10.1093/biomet/asv051 fatcat:lgbgqjujszfdvmq3fcvjcxoxva