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Nonlinear Time Series Prediction Based On A Power-Law Noise Model

Author

Listed:
  • FRANK EMMERT-STREIB

    (Stowers Institute for Medical Research, 1000 E. 50th Street, Kansas City, MO 64110, USA)

  • MATTHIAS DEHMER

    (Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria)

Abstract

In this paper we investigate the influence of a power-law noise model, also called Pareto noise, on the performance of a feed-forward neural network used to predict nonlinear time series. We introduce an optimization procedure that optimizes the parameters of the neural networks by maximizing the likelihood function based on the power-law noise model. We show that our optimization procedure minimizes themean squared errorleading to an optimal prediction. Further, we present numerical results applying our method to time series from the logistic map and the annual number of sunspots and demonstrate that a power-law noise model gives better results than a Gaussian noise model.

Suggested Citation

  • Frank Emmert-Streib & Matthias Dehmer, 2007. "Nonlinear Time Series Prediction Based On A Power-Law Noise Model," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 18(12), pages 1839-1852.
    • Handle: RePEc:wsi:ijmpcx:v:18:y:2007:i:12:n:s0129183107011765
    DOI: 10.1142/S0129183107011765
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    References listed on IDEAS

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    1. Nagahara, Yuichi, 2006. "Erratum to "A method of simulating multivariate nonnormal distributions by the Pearson distribution system and estimation" [Comput. Statist. Data Anal. 47 (2004) 1-29]," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2536-2535, June.
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    Cited by:

    1. Ran Wei & Qirui Gan & Huiquan Wang & Yue You & Xin Dang, 2020. "Short-term multiple power type prediction based on deep learning," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 11(4), pages 835-841, August.

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