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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 484093, 13 pages
Research Article

Online Sequential Prediction for Nonstationary Time Series with New Weight-Setting Strategy Using Extreme Learning Machine

1College of Computer and Information Engineering, Henan Normal University, Henan, Xinxiang 453007, China
2Management Institute, Xinxiang Medical University, Henan, Xinxiang 453003, China

Received 21 August 2014; Accepted 12 October 2014

Academic Editor: Amaury Lendasse

Copyright © 2015 Wentao Mao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Accurate and fast prediction of nonstationary time series is challenging and of great interest in both practical and academic areas. In this paper, an online sequential extreme learning machine with new weighted strategy is proposed for nonstationary time series prediction. First, a new leave-one-out (LOO) cross-validation error estimation for online sequential data is proposed based on inversion of block matrix. Second, a new weighted strategy based on the proposed LOO error estimation is proposed. This strategy ranks the samples’ importance by means of the LOO error of each new added sample and then assigns various weights. Performance comparisons of the proposed method with other existing algorithms are presented based on chaotic and real-world nonstationary time series data. The results show that the proposed method outperforms the classical ELM and OS-ELM in terms of generalization performance and numerical stability.