Neural Processing Letters

, Volume 43, Issue 3, pp 641–666 | Cite as

Identification of Lags in Nonlinear Autoregressive Time Series Using a Flexible Fuzzy Model

  • A. Veloz
  • R. Salas
  • H. Allende-Cid
  • H. Allende
  • C. Moraga


This work proposes a method to find the set of the most influential lags and the rule structure of a Takagi–Sugeno–Kang (TSK) fuzzy model for time series applications. The proposed method resembles the techniques that prioritize lags, evaluating the proximity of nearby samples in the input space using the closeness of the corresponding target values. Clusters of samples are generated, and the consistency of the mapping between the predicted variable and the set of candidate past values is evaluated. A TSK model is established, and possible redundancies in the rule base are avoided. The proposed method is evaluated using simulated and real data. Several simulation experiments were conducted for five synthetic nonlinear autoregressive processes, two nonlinear vector autoregressive processes and eight benchmark time series. The results show a competitive performance in the mean square error and a promising ability to find a proper set of lags for a given autoregressive process.


Lags identification Takagi–Sugeno–Kang fuzzy model  Nonlinear autoregressive time series Vector autoregressive time series Time series analysis 



This research was supported by FONDECYT 1110854, Basal FB 0821 CCTVal: FB/13HA/10, DIUV 64/2011, DGIP-UTFSM research Grants, and partially supported by the Foundation for the Advancement of Soft-Computing (Mieres, Spain) and by the CICYT (Spain) under Project TIN 2011-29827-C02-01.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • A. Veloz
    • 1
    • 2
  • R. Salas
    • 2
  • H. Allende-Cid
    • 3
  • H. Allende
    • 1
  • C. Moraga
    • 4
    • 5
  1. 1.Departamento de InformáticaUniversidad Técnica Federico Santa MaríaValparaísoChile
  2. 2.Escuela de Ingeniería BiomédicaUniversidad de ValparaísoValparaísoChile
  3. 3.Escuela de Ingeniería InformáticaPontificia Universidad Católica de ValparaísoValparaísoChile
  4. 4.European Centre for Soft ComputingMieresSpain
  5. 5.TU Dortmund UniversityDortmundGermany

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