Skip to main content
SpringerLink
Log in

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

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Abonyi J, Babuska R, Szeifert F (2002) Modified Gath-Geva fuzzy clustering for identification of Takagi–Sugeno fuzzy models. IEEE Trans Syst Man Cybern 32(5):612–621

    Article  Google Scholar 

  2. Abonyi J, Feil B (2007) Cluster analysis for data mining and system identification. Birkhäuser Verlag AG, Berlin

    MATH  Google Scholar 

  3. Abraham B, Ledolter J (1983) Time series analysis, forecasting and control, 3rd edn. Wiley, New York

    MATH  Google Scholar 

  4. Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19(6):716–723

    Article  MathSciNet  MATH  Google Scholar 

  5. Alizadeh M, Jolai F, Aminnayeri M, Rada R (2012) Comparison of different input selection algorithms in neuro-fuzzy modeling. Expert Syst Appl 1(39):1536–1544

    Article  Google Scholar 

  6. Allende H, Moraga C, Salas R (2002) Artificial neural networks in time series forecasting: a comparative approach. Kybernetika 38(6):685–707

    MathSciNet  MATH  Google Scholar 

  7. Bezdek JC (1981) Pattern recognition with fuzzy objective function algorithms. Plenum Press, New York

    Book  MATH  Google Scholar 

  8. Bolstad A, Van Veen B, Nowak R (2011) Causal network inference via group sparse regularization. IEEE Trans Signal Process 59(6):2628–2641

    Article  MathSciNet  Google Scholar 

  9. Bomberger JD, Seborg DE (1998) Determination of model order for NARX models directly from input-output data. J Process Control 8(5–6):459–468

    Article  Google Scholar 

  10. Boukezzoula R, Foulloy L, Galichet S (2006) Inverse controller design for fuzzy interval systems. IEEE Trans Fuzzy Syst 14(1):569–582

    Article  Google Scholar 

  11. Box GEP, Jenkins GM, Reinsel GC (1994) Time series analysis, forecasting and control, 3rd edn. Prentice Hall, Englewood Cliffs

    MATH  Google Scholar 

  12. Chen CLP, Wan JZ (1999) A rapid learning and dynamic stepwise updating algorithm for flat neural networks and the application to time-series prediction. IEEE Trans Syst Man Cybern 29(1):62–72

    Article  Google Scholar 

  13. Cheng Y, Wang L, Zeng J, Hu J (2011) Identification of quasi-ARX neurofuzzy model by using SVR-based approach with input selection. In: IEEE international conference on systems, man, and cybernetics, pp. 1585–1590

  14. Chiu SL (1996) Selecting input variables for fuzzy models. J Intell Fuzzy Syst 4(4):243–256

    Google Scholar 

  15. Cho J, Principe J, Erdogmus D, Motter M (2006) Modeling and inverse controller design for an unmanned aerial vehicle based on the self-organizing map. IEEE Trans Neural Netw 17(2):445–460

    Article  Google Scholar 

  16. Chuang CC, Su SF, Chen SS (2001) Robust TSK fuzzy modeling for function approximation with outliers. IEEE Trans Fuzzy Syst 9(6):810–821

    Article  Google Scholar 

  17. Claeskens G, Hjort NL (2008) Model selection and model averaging. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  18. Espinosa J, Vandewalle J, Wertz V (2005) Fuzzy logic, identification and predictive control. Springer, London

    MATH  Google Scholar 

  19. Feil B, Abonyi J, Szeifert F (2004) Model order selection of nonlinear input–output models—a clustering based approach. J Process Control 14(6):593–602

    Article  Google Scholar 

  20. Gan M, Peng H, Dong X (2012) A hybrid algorithm to optimize RBF network architecture and parameters for nonlinear time series prediction. Appl Math Model 36(7):2911–2919

    Article  MathSciNet  MATH  Google Scholar 

  21. Gan M, Peng H, Peng X, Inoussa G (2010) A locally linear RBF network-based state-dependent AR model for nonlinear time series modeling. Inf Sci 180(22):4370–4383

    Article  MathSciNet  Google Scholar 

  22. Gradisar D, Glavan M (2012) Input variable selection algorithms for HPC. In: IEEE international conference on industrial technology (ICIT), pp. 66–71

  23. Graves D, Pedrycz W (2009) Fuzzy prediction architecture using recurrent neural network. Neurocomputing 72:1668–1678

    Article  Google Scholar 

  24. Haufe S, Tomioka R, Nolte G, Müller K, Kawanabe M (2010) Modeling sparse connectivity between underlying brain sources for EEG/MEG. IEEE Trans Biomed Eng 57(8):1954–1963

    Article  Google Scholar 

  25. He X, Asada H (1993) A new method for identifying orders of input-output models for nonlinear dynamic systems. In: American control conference, pp. 2520–2523

  26. Jakubek S, Hametner C (2009) Identification of neurofuzzy models using GTLS parameter estimation. IEEE Trans Syst Man Cybern 39(5):1121–1133

    Article  Google Scholar 

  27. Jang JR (1993) ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cybern 23(3):665–685

    Article  Google Scholar 

  28. Jang JR (1996) Input selection for ANFIS learning. In: Proceedings of the Fifth IEEE international conference on fuzzy systems, pp. 1493–1499

  29. Kennel MB, Brown R, Abarbanel HD (1992) Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys Rev 45(6):3403–3411

    Article  Google Scholar 

  30. Lendasse A, Lee J, Wertz V, Verleysen M (2002) Forecasting electricity consumption using nonlinear projection and self-organizing maps. Neurocomputing 48(1):299–311

    Article  MATH  Google Scholar 

  31. Lin TN, Giles CL, Horne BG, Kung SY (1997) A delay damage model selection algorithm for NARX neural networks. IEEE Trans Signal Process 45(11):2719–2730

    Article  Google Scholar 

  32. Lin Y, Cunningham GA (1995) A new approach to fuzzy-neural system modeling. IEEE Trans Fuzzy Syst 3(2):190–198

    Article  Google Scholar 

  33. Lin Y, Cunningham GA, Coggeshall SV (1996) Input variable identification—fuzzy curves and fuzzy surfaces. Fuzzy Sets Syst 82(1):65–71

    Article  Google Scholar 

  34. Linkens DA, Chen MY (1999) Input selection and partition validation for fuzzy modelling using neural network. Fuzzy Sets Syst 107(3):299–308

    Article  MathSciNet  Google Scholar 

  35. Madeiros MC, Teräsvirta T, Rech G (2006) Building neural network models for time series: a statistical approach. J Forecast 25(1):49–75

    Article  MathSciNet  Google Scholar 

  36. Mandic D, Chambers J (2001) Recurrent neural networks for prediction: learning algorithms, architectures and stability. Wiley, New York

    Book  Google Scholar 

  37. Martinetz TM, Berkovich SG, Schulten KJ (1993) Neural-gas network for vector quantization and its application to time-series prediction. IEEE Trans Neural Netw 4(4):558–569

    Article  Google Scholar 

  38. Montesino F, Barriga A (2010) Automatic clustering-based identification of autoregressive fuzzy inference models for time series. Neurocomputing 73(10):1937–1949

    Google Scholar 

  39. Moraga C, Trillas E, Guadarrama S (2003) Multiple-valued logic and artificial intelligence. Basics of fuzzy control revisited. Artif Intell Rev 20(3–4):169–197

    Article  MATH  Google Scholar 

  40. Pal N, Pal K, Keller J, Bezdek JC (2005) A possibilistic fuzzy c-means clustering algorithm. IEEE Trans Fuzzy Syst 13(14):517–530

    Article  MathSciNet  Google Scholar 

  41. Pedrycz W, Gomide F (1998) An introduction to fuzzy sets: analysis and design. The MIT Press, Cambridge

    MATH  Google Scholar 

  42. Pi H, Peterson C (1994) Finding the embedding dimension and variable dependencies in time series. Neural Comput 6(3):509–520

    Article  Google Scholar 

  43. Qiao J, Wang H (2008) A self-organizing fuzzy neural network and its applications to function approximation and forecast modeling. Neurocomputing 71:564–569

    Article  Google Scholar 

  44. Quinn C, Kiyavash N, Coleman T (2011) A minimal approach to causal inference on topologies with bounded indegree. In: 50th IEEE conference on decision and control and European control conference

  45. Rech G, Teräsvirta T, Tschernig T (2001) A simple variable selection technique for nonlinear models. Commun Stat Theory Methods 30:1227–1241

    Article  MathSciNet  MATH  Google Scholar 

  46. Remache C, Maamri R, Sahnoun Z (2012) Structure identification for complex systems and inference interpretable rules. In: Sixth international conference on complex, intelligent and software intensive systems, pp. 836–840

  47. Rhodes C, Morari M (1998) Determining the model order of nonlinear input/output systems. AIChE J 44(1):151–163

    Article  Google Scholar 

  48. Saez D, Cipriano A (1999) Fuzzy modelling for a combined cycle power plant. In: Proceedings of the IEEE international conference on fuzzy systems (FUZZ-IEEE ’99), pp. 1186–1190

  49. Salas R (2010) Robustness and flexibility analysis of the learning algorithms of artificial neural networks. PhD thesis, Departamento de Informática, Universidad Técnica Federico Santa María

  50. Sanandaji BM, Vincent TL, Wakin MB (2011) Compressive topology identification of interconnected dynamic systems via clustered orthogonal matching pursuit. In: 50th IEEE conference on decision and control and European control conference

  51. Souza LGM, Barreto GA (2010) On building local models for inverse system identification with vector quantization algorithms. Neurocomputing 73(10–12):1993–2005

    Article  Google Scholar 

  52. Sugeno M, Yasukawa T (1993) A fuzzy-logic-based approach to qualitative modeling. IEEE Trans Fuzzy Syst 1(1):7–31

    Article  Google Scholar 

  53. Tung WL, Quek C (2002) GenSoFNN: a generic self-organizing fuzzy neural network. IEEE Trans Neural Netw 13(5):1075–1085

    Article  Google Scholar 

  54. Veloz A, Allende-Cid H, Allende H, Moraga C, Salas R (2009) A flexible neuro-fuzzy autoregressive technique for non-linear time series forecasting. LNCS 5711:22–29

    Google Scholar 

  55. Šindelař R, Babuška R (2004) Input selection for nonlinear regression models. IEEE Trans Fuzzy Syst 12(5):688–696

    Article  Google Scholar 

Download references

Acknowledgments

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.

Author information

Authors and Affiliations

  1. Departamento de Informática, Universidad Técnica Federico Santa María, Valparaíso, Chile

    A. Veloz & H. Allende

  2. Escuela de Ingeniería Biomédica, Universidad de Valparaíso, Valparaíso, Chile

    A. Veloz & R. Salas

  3. Escuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile

    H. Allende-Cid

  4. European Centre for Soft Computing, 33600, Mieres, Spain

    C. Moraga

  5. TU Dortmund University, 44221, Dortmund, Germany

    C. Moraga

Authors
  1. A. Veloz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Salas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Allende-Cid
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. H. Allende
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. C. Moraga
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Veloz.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Veloz, A., Salas, R., Allende-Cid, H. et al. Identification of Lags in Nonlinear Autoregressive Time Series Using a Flexible Fuzzy Model. Neural Process Lett 43, 641–666 (2016). https://doi.org/10.1007/s11063-015-9438-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-015-9438-1

Keywords

Search

Navigation