Laplace approximation with Gaussian Processes for volatility forecasting

Generalized Autoregressive Conditional Heteroscedascity (GARCH) models are ad hoc methods very used to predict volatility in financial time series. On the other hand, Gaussian Processes (GPs) offer very good performance for regression and prediction tasks, giving estimates of the average and dispersion of the predicted values, and showing resilience to overfitting. In this paper, a GP model is proposed to predict volatility using a reparametrized form of the Ornstein-Uhlenbeck covariance function, which reduces the underlying latent function to be an AR(1) process, suitable for the Brownian motion typical of financial time series. The tridiagonal character of the inverse of this covariance matrix and the Laplace method proposed to perform inference allow accurate predictions at a reduced cost compared to standard GP approaches. The experimental results confirm the usefulness of the proposed method to predict volatility, outperforming GARCH models with more accurate forecasts and a lower computational burden.