We investigate the benefits of feature selection, nonlinear modelling and online learning when forecasting in financial time series. We consider the sequential and continual learning sub-genres of online learning. The experiments we conduct show that there is a benefit to online transfer learning, 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 networks, are able to outperform a random walk baseline, whereas the offline learning models struggle to do so.
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