Adaptive Ensemble Models of Extreme Learning Machines for Time Series Prediction

In time series prediction, one does often not know the properties of the underlying system generating the time series. For example, is it a closed system that is generating the time series or are there any external factors influencing the system? As a result of this, you often do not know beforehand whether a time series is stationary or nonstationary, and in the ideal case you do not want to make any assumptions about this. Therefore, if one wants to do time series prediction on such a system it would be nice if a model exists that is able to perform well on both nonstationary and stationary time series, and that the model adapts itself to the environment in which it is applied. In this thesis, we will experimentally investigate a method that hopefully has this property. We will look at the application of adaptive ensemble models of Extreme Learning Machines (ELMs) to the problem of one-step ahead prediction in (non)stationary time series. In the experiments, we verify that the model works on a stationary time series, the Santa Fe Laser Data time series. Furthermore, we test the adaptivity of the ensemble model on a nonstationary time series, the Quebec Births time series. We show that the adaptive ensemble model can achieve a test error comparable to or better than a state-of-the-art method like LS-SVM, while at the same time, it remains adaptive. Additionally, the adaptive ensemble model has low computational cost. keywords: time series prediction, sliding window, extreme learning machine, ensemble models, nonstationarity, adaptivity