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

A new direct approach of computing multi-step ahead predictions for non-linear time series is introduced. The covariance of the parameter estimates associated with, and the mean squared k -step ahead prediction errors of the new direct approach are smaller than those obtained using the conventional direct approach. Numerical examples are included to illustrate the application of the new direct approach.

[1]  John Ringwood,et al.  Incorporation of statistical methods in multi-step neural network prediction models , 1998, 1998 IEEE International Joint Conference on Neural Networks Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36227).

[2]  Sheng Chen,et al.  Recursive prediction error parameter estimator for non-linear models , 1989 .

[3]  Sheng Chen,et al.  Orthogonal least squares methods and their application to non-linear system identification , 1989 .

[4]  C. Granger,et al.  Forecasting from non-linear models in practice , 1994 .

[5]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[6]  D. Findley,et al.  Model Selection for Multi-Step-Ahead Forecasting , 1985 .

[7]  Paul Kabaila,et al.  Estimation based on one step ahead prediction versus estimation based on multi-step ahead prediction , 1981 .

[8]  Piet M. T. Broersen,et al.  Autoregressive model orders for Durbin's MA and ARMA estimators , 2000, IEEE Trans. Signal Process..

[9]  Sheng Chen,et al.  Extended model set, global data and threshold model identification of severely non-linear systems , 1989 .

[10]  M. Gabr.  ON THE THIRD‐ORDER MOMENT STRUCTURE AND BISPECTRAL ANALYSIS OF SOME BILINEAR TIME SERIES , 1988 .

[11]  Mahmoud M. Gabr,et al.  THE ESTIMATION AND PREDICTION OF SUBSET BILINEAR TIME SERIES MODELS WITH APPLICATIONS , 1981 .

[12]  Sheng Chen,et al.  Practical identification of NARMAX models using radial basis functions , 1990 .

[13]  H. Tong.  Non-linear time series. A dynamical system approach , 1990 .

[14]  J. A. Lane,et al.  FORECASTING EXPONENTIAL AUTOREGRESSIVE MODELS OF ORDER 1 , 1989 .

[15]  D. Rumelhart,et al.  Predicting sunspots and exchange rates with connectionist networks , 1991 .

[16]  Arye Nehorai,et al.  On multistep prediction error methods for time series models , 1989 .

[17]  Zhidong Bai,et al.  MULTI-STEP PREDICTION FOR NONLINEAR AUTOREGRESSIVE MODELS BASED ON EMPIRICAL DISTRIBUTIONS , 1999 .

[18]  Michael Y. Hu,et al.  Forecasting with artificial neural networks: The state of the art , 1997 .

[19]  J. Durbin.  EFFICIENT ESTIMATION OF PARAMETERS IN MOVING-AVERAGE MODELS , 1959 .

[20]  John. Pemberton.  EXACT LEAST SQUARES MULTI‐STEP PREDICTION FROM NONLINEAR AUTOREGRESSIVE MODELS , 1987 .

[21]  I. J. Leontaritis,et al.  Input-output parametric models for non-linear systems Part II: stochastic non-linear systems , 1985 .

[22]  Amir F. Atiya,et al.  A comparison between neural-network forecasting techniques-case study: river flow forecasting , 1999, IEEE Trans. Neural Networks.

[23]  Carlo Novara,et al.  Nonlinear Time Series , 2003 .

[24]  Amir F. Atiya,et al.  Multi-step-ahead prediction using dynamic recurrent neural networks , 2000, Neural Networks.

[25]  Shang-Liang Chen,et al.  Orthogonal least squares learning algorithm for radial basis function networks , 1991, IEEE Trans. Neural Networks.

[26]  Sheng Chen,et al.  Modelling and analysis of non-linear time series , 1989 .

[27]  Bryan W. Brown,et al.  Predictors in Dynamic Nonlinear Models: Large-Sample Behavior , 1989, Econometric Theory.

[28]  Stephen A. Billings,et al.  Nonlinear model validation using correlation tests , 1994 .