Inference in Infinite Superpositions of Non-Gaussian Ornstein–Uhlenbeck Processes Using Bayesian Nonparametic Methods

This paper describes a Bayesian nonparametric approach to volatility estimation. Volatility is assumed to follow a superposition of an infinite number of Ornstein–Uhlenbeck processes driven by a compound Poisson process with a parametric or nonparametric jump size distribution. This model allows a wide range of possible dependencies and marginal distributions for volatility. The properties of the model and prior specification are discussed, and a Markov chain Monte Carlo algorithm for inference is described. The model is fitted to daily returns of four indices: the Standard and Poors 500, the NASDAQ 100, the FTSE 100, and the Nikkei 225.