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Time series prediction using kernel adaptive filter with least mean absolute third loss function

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Abstract

In this paper, a novel kernel adaptive filter, based on the least mean absolute third (LMAT) loss function, is proposed for time series prediction in various noise environments. Combining the benefits of the kernel method and the LMAT loss function, the proposed KLMAT algorithm performs robustly against noises with different probability densities. However, an important limitation of the KLMAT algorithm is a trade-off between the convergence rate and steady-state prediction error imposed by the selection of a certain value for the learning rate. Therefore, a variable learning rate version (VLR–KLMAT algorithm) is also proposed based on a Lorentzian function. We analyze the stability and convergence behavior of the KLMAT algorithm and derive a sufficient condition to predict its learning rate behavior. Moreover, a kernel recursive extension of the KLMAT algorithm is further proposed for performance improvement. Simulation results in the context of time series prediction verify the effectiveness of the proposed algorithms.

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Acknowledgements

The authors want to express their deep thanks to the anonymous reviewers for many valuable comments which greatly helped to improve the quality of this work. This work was partially supported by National Science Foundation of P.R. China (Grant: 61571374, 61271340, 61433011). The first author would like to acknowledge the China Scholarship Council (CSC) for providing him with financial support to study abroad (No. 201607000050).

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  1. School of Electrical Engineering, Southwest Jiaotong University, Chengdu, China

    Lu Lu & Haiquan Zhao

  2. School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an, China

    Badong Chen

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  1. Lu Lu
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  2. Haiquan Zhao
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Correspondence to Haiquan Zhao.

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Lu, L., Zhao, H. & Chen, B. Time series prediction using kernel adaptive filter with least mean absolute third loss function. Nonlinear Dyn 90, 999–1013 (2017). https://doi.org/10.1007/s11071-017-3707-7

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