Time series prediction and online learning

We present a series of theoretical and algorithmic results combining the benefits of the statistical learning approach to time series prediction with that of on-line learning. We prove new generalization guarantees for hypotheses derived from regret minimization algorithms in the general scenario where the data is generated by a non-stationary non-mixing stochastic process. Our theory enables us to derive model selection techniques with favorable theoretical guarantees in the scenario of time series, thereby solving a problem that is notoriously difficult in that scenario. It also helps us devise new ensemble methods with favorable theoretical guarantees for the task of forecasting non-stationary time series.