Boosting GARCH and neural networks for the prediction of heteroskedastic time series

This work develops and evaluates new algorithms based on GARCH models, neural networks and boosting techniques, designed to model and predict heteroskedastic time series. The main novel elements of these new algorithms are as follows: (a) in regard to neural networks, the simultaneous estimation of the conditional mean and volatility through the maximization of likelihood; (b) in regard to boosting, its simultaneous application to mean and variance components of the likelihood, and the use of likelihood-based models (e.g., GARCH) as the base hypothesis rather than gradient fitting techniques using least squares. The behavior of the proposed algorithms is evaluated over simulated data and over the Standard & Poor’s 500 Index returns series, resulting in frequent and significant improvements in relation to the ARMA-GARCH models.