Gaussian Process Regression Stochastic Volatility Model for Financial Time Series

Traditional economic models have rigid-form transition functions when modeling time-varying volatility of financial time series data and cannot capture other time-varying dynamics in the financial market. In this paper, combining the Gaussian process state-space model framework and the stochastic volatility (SV) model, we introduce a new Gaussian process regression stochastic volatility (GPRSV) model building procedures for financial time series data analysis and time-varying volatility modeling. The GPRSV extends the SV model. The flexible stochastic nature of the Gaussian process state description allows the model to capture more time-varying dynamics of the financial market. We also present the model estimation methods for the GPRSV model. We demonstrate the superior volatility prediction performance of our model with both simulated and empirical financial data.