Paper:
Gaussian Process Volatility Model
The prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the evolution of the variance. Moreover, functional parameters are usually learned by maximum likelihood, which can lead to overfitting. To address these problems we introduce GP-Vol, a novel non-parametric model for time-changing variances based on Gaussian Processes. This new model can capture highly flexible functional relationships for the variances. Furthermore, we introduce a new online algorithm for fast inference in GP-Vol. This method is much faster than current offline inference procedures and it avoids overfitting problems by following a fully Bayesian approach. Experiments with financial data show that GP-Vol performs significantly better than current standard alternatives.

Review:
This paper proposes a new nonparametric volatility model.The contribution of the paper relies on the application of Gaussian process prior to stochastic volatility models. The inference approach is based on SMC and is a straightforward application of the Liu and West's APF algorithm.The literature review lacks of some important references and the empirical comparison is not complete. My major concerns are the following:\begin{enumerate}\item The authors proposed a new stochastic volatility (SV) model, but in the introduction and in the paper there is no reference (e.g., Taylor (1987), Jacquier, Polson, Rossi (1994, 2004) to this class of models.\item A comparison is proposed between GP-Vol and GARCH models, but the increased flexibility of a SV over the GARCH family has already been proved in the literature by many parts. See e.g. Fridman and Harris (1998). Thus I would strongly suggest the inclusion of a comparison between a standard SV model and the proposed GP-Vol model.\item The author proposed a new nonparametric model, but no references is give to the recent advances in Bayesian nonparametric which make use of flexible prior processes such as Dirichlet processes (e.g., see Bassetti, Casarin, Leisen (2014), Griffin (2011), Griffin and Steel (2011)). \end{enumerate}References:\begin{itemize}\item Jacquier, E., Polson, N., Rossi, P., 1994. Bayesian analysis of stochastic volatility models (with discussion). Journal of Business and Economic Statistics 12 (4), 371-417.\item Jacquier, E., Polson, N., Rossi, P., 1994. Bayesian analysis of stochastic volatility models with fat-tails and correlated errors. Journal of Econometrics 122, 185-212.\item Fridman, M., Harris, L., 1998. A maximum likelihood approach for non-Gaussian stochastic volatility models.Journal of Business and Economics Statistics 16 (3), 284-291.\item Bassetti, F., Casarin, R., Leisen, F. (2014), Pitman-Yor Process Prior for Bayesian Inference, Journal of Econometrics, 180, 49-72. \item J. E. Griffin. Inference in infinite superpositions of non-Gaussian Ornstein-Uhlenbeck processesusing Bayesian nonparametic methods. Journal of Financial Econometrics, 1:1-31, 2011.\item J. E. Griffin and M. F. J. Steel. Stick-breaking autoregressive processes. Journal of Econometrics, 162:383-396, 2011.\end{itemize}