Abstract: The present invention relates to methods and systems for learning online to predict time-series data. More specifically, the present invention discloses a system that takes at least one time-varying signal as input, and use a model with an adjustable set of parameters to predict the future values of this time-varying signal as output. The system maintains a compressed representation of the history of its predicted output values, and a learning rule is used to compute an update to the system's parameters so as to reduce any discrepancy between the current value of the time varying signal and all previous predictions for this value that are stored in the compressed representation. The system is operated to perform at least one robotic control, pattern classification, signal processing, or data generation task that is improved by predicting the future values of a time-varying input signal.