Advanced search
Publication Cover
International Journal of Control Volume 76, 2003 - Issue 8
Submit an article Journal homepage
102
Views
10
CrossRef citations to date
0
Altmetric
Original Articles

A new direct approach of computing multi-step ahead predictions for non-linear models

K. L. Lee Department of Automatic Control and Systems Engineering, Mappin Street, Sheffield, S1 3JD, UK
&
S. A. Billings Department of Automatic Control and Systems Engineering, Mappin Street, Sheffield, S1 3JD, UK
Pages 810-822 | Published online: 08 Nov 2010

  • AL-QASSAM , M. S. and LANE , L.A. 1989 . Forecasting exponential autoregressive models of order (1) . Journal of Time Series Analysis , 10 : 95 – 113 .
  • ATIYA , A. F. , SUZAN , M. , EL-SHOURA , S. , SHABEEN , I. and EL-SHERIF , M. S. 1999 . A comparison between neural-network forecasting techniques-case study: river flow forecasting . IEEE Transaction on Neural Networks , 10 : 402 – 409 .
  • BILLINGS , S. A. and CHEN , S. 1989 . Extended model set, global data and threshold model identification of severely non-linear systems . International Journal of Control , 50 : 1897 – 1923 .
  • BILLINGS , S. A. and ZHU , Q. M. 1994 . Nonlinear model validation using the correlation tests . International Journal of Control , 60 : 1107 – 1120 .
  • Box , G. E. P. , JENKINS , G. M. and REINSEL , G. C. 1994 . Time Series Analysis, , 3rd edn , Englewood Cliffs, New Jersey : Prentice Hall .
  • BROERSEN , P. M.T. 2000 . Autoregressive model orders for Durbin's MA and ARMA estimators . IEEE Transaction on Signal Processing , 48 : 2454 – 2457 .
  • BROWN , B. and MARIANO , R. 1989 . Predictors in dynamic non-linear models: large sample behaviour . Econometric Theory , 5 : 430 – 452 .
  • CHEN , S. and BILLINGS , S. A. 1989a . Modelling and analysis of non-linear time series . International Journal of Control , 50 : 2151 – 2171 .
  • CHEN , S. and BILLINGS , S. A. 1989b . Recursive prediction error parameter estimator for non-linear models . International Journal of Control , 49 : 569 – 594 .
  • CHEN , S. , BILLINGS , S. A. , COWAN , C. F. N. and GRANT , P. M. 1990 . Practical identification of NARMAX models using radial basis functions . International Journal of Control , 52 : 1327 – 1350 .
  • CHEN , S. , BILLINGS , S. A. and LUO , W. 1989 . Orthogonal least squares method and their applications to non-linear system identification . International Journal of Control , 50 : 1873 – 1896 .
  • CHEN , S. , COWAN , C. F. N. and GRANT , P. M. 1991 . Orthogonal least squares learning algorithm for radial basis function network . IEEE Transaction of Neural Networks , 2 : 302 – 309 .
  • CLOAREC , G. and RINGWOOD , J. Incorporation of statistical methods in multi-step neural network prediction models . Proceedings of the 1998 IEEE International Joint Conference on Neural Networks . Anchorage, AK, USA. pp. 2513 – 2518 .
  • DURBIN , J. 1959 . Efficient estimation of parameters in moving average models . Biometrika , 46 : 306 – 316 .
  • FINDLEY , D. F. Model selection for multi-step-ahead forecasting . Prep, of 7th IFAC/IFORS Symposium on Identification and System Parameter Estimation . 1985 , York, UK. Edited by: Barker , H. A. and Yound , P. C. pp. 1039 – 1044 .
  • GABR , M. M. and RAO , T. S. 1981 . The estimation and prediction of subset bilinear time series models with applications . Journal of Time Series Analysis , 9 : 11 – 20 .
  • GUO , M. , BAI , Z. and AN , H. Z. 1999 . Multi-step prediction for nonlinear autoregressive models based on empirical distributions . Statistica Sinica , 9 : 559 – 570 .
  • KABAILA , P. V. 1981 . Estimation based on one-step ahead prediction versus estimation based on multi-step ahead prediction . Stochastics , 6 : 43 – 55 .
  • LEONTARITIS , I. J. and BILLINGS , S. A. 1985a . Input-output parametric models for non-linear systems part I: deterministic nonlinear systems . International Journal of Control , 41 : 303 – 328 .
  • LEONTARITIS , I. J. and BILLINGS , S. A. 1985b . Input-output parametric models for nonlinear systems part II: stochastic nonlinear systems . International Journal of Control , 41 : 329 – 344 .
  • LIN , J. L. and GRANGER , C. W. J. 1994 . Forecasting from non-linear models in practice . Journal of Forecasting , 13 : 1 – 9 .
  • PARLOS , A. G. , RAIS , O. T. and ATIYA , A. F. 2000 . Multi-step-ahead prediction using dynamic recurrent neural networks . Neural Networks , 13 : 765 – 786 .
  • PEMBERTON , J. 1987 . Exact least squares multi-step prediction from nonlinear autoregressive models . Journal of Tune Series Analysis , 8 : 443 – 448 .
  • SÖDERSTRÖM , T. and STOICA , P. 1989 . System Identification , Prentice Hall .
  • STOICA , P. and NEHORAI , A. 1989 . On multistep prediction error methods for time series models . Journal of Forecasting , 8 : 357 – 368 .
  • TONG , H. 1990 . Nonlinear Time Series, A Dynamical System Approach , Oxford, OK : Clarendon Press .
  • WEIGEND , A. S. , HUBERMAN , B. A. and RUMELHART , D. E. 1992 . “ Predicting sunspots and exchange rates with connectionist networks ” . In Nonlinear Modeling and Forecasting , Edited by: Casdagli , M. and Eubank , S. 395 – 432 . Redwood City, CA : Addison-Wesley .
  • ZHANG , G. , PATUWO , B. E. and HU , M. Y. 1998 . Forecasting with artificial neural networks: The state of the art . International Journal of Forecasting , 14 : 35 – 62 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.