Efficient Bayesian inference for stochastic volatility models with ensemble MCMC methods

In this paper, we introduce efficient ensemble Markov Chain Monte Carlo (MCMC) sampling methods for Bayesian computations in the univariate stochastic volatility model. We compare the performance of our ensemble MCMC methods with an improved version of a recent sampler of Kastner and Fruwirth-Schnatter (2014). We show that ensemble samplers are more efficient than this state of the art sampler by a factor of about 3.1, on a data set simulated from the stochastic volatility model. This performance gain is achieved without the ensemble MCMC sampler relying on the assumption that the latent process is linear and Gaussian, unlike the sampler of Kastner and Fruwirth-Schnatter. The stochastic volatility model is a widely-used example of a state space model with non-linear or non-Gaussian transition or observation distributions. It models observed log-returns y = (y1,..., yN) of a financial time series with time-varying volatility, as follows: Yi|xi ∼ N(0, exp(c+ σxi)), i = 1,..., N (1) X1 ∼ N(0, 1/(1 − φ2)) (2