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Cluster-weighted modelling for time-series analysis

Author

Listed:
  • N. Gershenfeld

    (Physics and Media Group, MIT Media Laboratory)

  • B. Schoner

    (Physics and Media Group, MIT Media Laboratory)

  • E. Metois

    (Physics and Media Group, MIT Media Laboratory
    ARIS Technologies)

Abstract

The need to characterize and forecast time series recurs throughout the sciences, but the complexity of the real world is poorly described by the traditional techniques of linear time-series analysis. Although newer methods can provide remarkable insights into particular domains, they still make restrictive assumptions about the data, the analyst, or the application1. Here we show that signals that are nonlinear, non-stationary, non-gaussian, and discontinuous can be described by expanding the probabilistic dependence of the future on the past around local models of their relationship. The predictors derived from this general framework have the form of the global combinations of local functions that are used in statistics2,3,4, machine learning5,6,7,8,9,10 and studies of nonlinear dynamics11,12. Our method offers forecasts of errors in prediction and model estimation, provides a transparent architecture with meaningful parameters, and has straightforward implementations for offline and online applications. We demonstrate our approach by applying it to data obtained from a pseudo-random dynamical system, from a fluctuating laser, and from a bowed violin.

Suggested Citation

  • N. Gershenfeld & B. Schoner & E. Metois, 1999. "Cluster-weighted modelling for time-series analysis," Nature, Nature, vol. 397(6717), pages 329-332, January.
    • Handle: RePEc:nat:nature:v:397:y:1999:i:6717:d:10.1038_16873
    DOI: 10.1038/16873
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    Cited by:

    1. Francesca Torti & Domenico Perrotta & Marco Riani & Andrea Cerioli, 2019. "Assessing trimming methodologies for clustering linear regression data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(1), pages 227-257, March.
    2. Salvatore D. Tomarchio & Paul D. McNicholas & Antonio Punzo, 2021. "Matrix Normal Cluster-Weighted Models," Journal of Classification, Springer;The Classification Society, vol. 38(3), pages 556-575, October.
    3. Yau, Her-Terng & Chen, Chieh-Li, 2006. "Chattering-free fuzzy sliding-mode control strategy for uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 709-718.
    4. Francesca Torti & Marco Riani & Gianluca Morelli, 2021. "Semiautomatic robust regression clustering of international trade data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 863-894, September.
    5. Salvatore Ingrassia & Simona Minotti & Giorgio Vittadini, 2012. "Local Statistical Modeling via a Cluster-Weighted Approach with Elliptical Distributions," Journal of Classification, Springer;The Classification Society, vol. 29(3), pages 363-401, October.
    6. Giorgio Vittadini & Simona Caterina Minotti, 2005. "A methodology for measuring the relative effectiveness of healthcare services," Working Papers 20050401, Università degli Studi di Milano-Bicocca, Dipartimento di Statistica.
    7. Ferreira, Fernando F & Francisco, Gerson & Machado, Birajara S & Muruganandam, Paulsamy, 2003. "Time series analysis for minority game simulations of financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 321(3), pages 619-632.

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