Before revision:  We also find that , in the subset of models we use , sequential learning in time with online Ridge regression, provides the best next step ahead forecasts, and continual learning with an online radial basis function network, provides the best multi-step ahead forecasts.
After revision:  We also find that , in the form of radial basis function networks, beyond the sequential updating of recursive least-squares models. We show that the radial basis function networks, which make use of clustering algorithms to construct a kernel Gram matrix, are more beneficial than treating each training vector as separate basis functions, as occurs with kernel Ridge regression. We demonstrate quantitative procedures to determine the very structure of the radial basis function networks. Finally, we conduct experiments on the log returns of financial time series and show that the online learning models, particularly the radial basis function network, provides the best multi-step ahead forecasts.