Financial time series volatility analysis using Gaussian process state-space models

In this paper, we propose a novel nonparametric modeling framework for financial time series data analysis, and apply it to the problem of time varying volatility modeling. Existing parametric models have a rigid-form transition function and they often have over-fitting problems when model parameters are estimated using maximum likelihood methods. These drawbacks effect the models´ prediction performance. To solve this problem, we take Bayesian nonparametric modeling approach. By adding Gaussian process prior to the hidden state transition process, we extend the standard state-space model to a Gaussian process state-space model. We introduce the Gaussian process regression stochastic volatility (GPRSV) model and instead of using maximum likelihood methods, we use Monte Carlo inference algorithms. We demonstrate performance of our model and inference methods with both simulated and empirical financial data.