Long term prediction of non-linear time series using multiresolution wavelet models

References

• Allingham , D , West , M and Mees , A . 1998 . Wavelet reconstruction of non-linear dynamics . International Journal of Bifurcation and Chaos , 8 : 2191 – 2201 .
   Google Scholar
• Atiya , A , El-Shura , SM , Shaheen , SI and El-Sherif , SM . 1999 . A comparison between neural-network forecasting techniques—case study: river flow forecasting . IEEE Transactions on Neural Networks , 10 : 402 – 409 .
   PubMed Web of Science ®Google Scholar
• Bhansali , RJ . 1997 . Direct autoregressive predictions for multistep prediction: order selection and performance relative to the plug in predictors . Statistica Sinca , 7 : 425 – 449 .
   Web of Science ®Google Scholar
• Billings , SA and Chen , S . 1998 . “ The determination of multivariable non-linear models for dynamic systems using neural networks ” . In Neural Network Systems Techniques and Applications , Edited by: Leondes , CT . 231 – 278 . San Diego : Academic Press .
   Google Scholar
• Billings , SA and Coca , D . 1999 . Discrete wavelet models for identification and qualitative analysis of chaotic systems . International Journal of Bifurcation and Chaos , 9 : 1263 – 1284 .
   Web of Science ®Google Scholar
• Billings , SA and Tao , QH . 1991 . Model validation tests for non-linear signal processing applications . International Journal of Control , 54 : 235 – 244 .
   Google Scholar
• Billings , SA and Wei , HL . 2005 . The wavelet-NARMAX representation: a hybrid model structure combining polynomial models and multiresolution wavelet decompositions . International Journal of Systems Science , 36 : 137 – 152 .
   Web of Science ®Google Scholar
• Billings , SA , Korenberg , M and Chen , S . 1988 . Identification of non-linear output-affine systems using an orthogonal least-squares algorithm . International Journal of Systems Science , 19 : 1559 – 1568 .
   Web of Science ®Google Scholar
• Box , GEP and Jenkins , GM . 1976 . Time Series Analysis: Forecasting and Control , San Francisco, CA : Holden-Day .
   Google Scholar
• Cao , LY , Hong , YG , Fang , HP and He , GW . 1995 . Predicting chaotic time series with wavelet networks . Physica D , 85 : 225 – 238 .
   Google Scholar
• Casdagli , M . 1989 . Non-linear prediction of chaotic time series . Physica D , 35 : 335 – 356 .
   Web of Science ®Google Scholar
• Chen , ZH . 1993 . Fitting multivariate regression functions by interaction spline models . Journal of the Royal Statistical Society, Series B (Methodological) , 55 : 473 – 491 .
   Google Scholar
• Chen , S and Billings , SA . 1989 . Modelling and analysis of non-linear time series . International Journal of Control , 50 : 2151 – 2171 .
   Web of Science ®Google Scholar
• Chen , S , Billings , SA and Luo , W . 1989 . Orthogonal least squares methods and their application to non-linear system identification . International Journal of Control , 50 : 1873 – 1896 .
   Web of Science ®Google Scholar
• Chui , CK . 1992 . An Introduction to Wavelets , Boston : Academic Press .
   Google Scholar
• Coca , D and Billings , SA . 1997 . Continuous-time system identification for linear and non-linear system identification using wavelet decompositions . International Journal of Bifurcation and Chaos , 7 : 87 – 96 .
   Web of Science ®Google Scholar
• Daubechies , I . 1992 . Ten Lectures on Wavelets , Philadelphia, Pennsylvania : Society for Industrial and Applied Mathematics .
   Google Scholar
• Fan , JQ and Yao , QW . 2005 . Non-linear Time Series: Nonparametric and Parametric Methods , New York : Springer .
   Google Scholar
• Farmer , JD and Sidorowich , JJ . 1987 . Predicting chaotic time series . Physical Review Letters , 59 : 845 – 848 .
   PubMed Web of Science ®Google Scholar
• Friedman , JH . 1991 . Multivariate adaptive regression splines . The Annals of Statistics , 19 : 1 – 67 .
   Web of Science ®Google Scholar
• Ghanem , R and Romeo , F . 2001 . A wavelet-based approach for model and parameter identification of non-linear systems . International Journal of Non-Linear Mechanics , 36 : 835 – 859 .
   Web of Science ®Google Scholar
• Golub , GH , Heath , M and Wahha , G . 1979 . Generalized cross-validation as a method for choosing a good ridge parameter . Technometrics , 21 : 215 – 223 .
   Web of Science ®Google Scholar
• Hill , T , Marquez , L , O’Connor , M and Remus , W . 1994 . Artificial neural networks for forecasting and decision making . International Journal of Forecasting , 10 : 5 – 15 .
   Web of Science ®Google Scholar
• Ing , C-K . 2003 . Multistep prediction in autoregressive processes . Econometric Theory , 19 : 254 – 279 .
   Web of Science ®Google Scholar
• Jimenez , J , Moreno , JA and Ruggeri , GJ . 1992 . Forecasting on chaotic time series: a local optimal linear reconstruction method . Physics Reviewer A , 45 : 3553 – 3558 .
   PubMedGoogle Scholar
• Judd , K and Small , M . 2000 . Towards long-term prediction . Physica D , 136 : 31 – 44 .
   Google Scholar
• Korenberg , M , Billings , SA , Liu , YP and McIlroy , PJ . 1988 . Orthogonal parameter estimation algorithm for non-linear stochastic systems . International Journal of Control , 48 : 193 – 210 .
   Web of Science ®Google Scholar
• Lee , KL and Billings , SA . 2003 . A new direct approach of computing multi-step ahead predictions for non-linear models . International Journal of Control , 76 : 810 – 822 .
   Web of Science ®Google Scholar
• Lin , TN , Horne , BG , Tino , P and Giles , CL . 1996 . Learning long-term dependencies in NARX recurrent neural networks . IEEE Transactions on Neural Networks , 7 : 1329 – 1338 .
   PubMed Web of Science ®Google Scholar
• Mackey , MC and Glass , L . 1977 . Oscillation and chaos in physiological control systems . Science , 197 : 287 – 289 .
   PubMed Web of Science ®Google Scholar
• Mallat , SG . 1989 . A theory for multiresolution signal decomposition: the wavelet representation . IEEE Transactions on Pattern Analysis and Machine Intelligence , 11 : 674 – 693 .
   Web of Science ®Google Scholar
• Marcellino , M , Stock , JH and Watson , MW . 2004 . “ A comparison of direct and iterated multistep AR methods for forecasting macroeconomic time series ” . [http://ksghome.harvard.edu/~JStock/papers.htm]
   Google Scholar
• McNames , J . 2002 . Local averaging optimization for chaotic time series prediction . Neurocomputing , 48 : 279 – 297 .
   Google Scholar
• Meyer , Y . 1993 . Wavelets: Algorithms and Applications , Philadelphia, Pennsylvania : SIAM .
   Google Scholar
• Pandit , SM and Wu , SM . 1983 . Time Series and System Analysis with Applications , New York : Wiley & Sons .
   Google Scholar
• Parlos , AG , Rais , OT and Atiya , AF . 2000 . Multi-step-ahead prediction using dynamic recurrent neural networks . Neural Networks , 13 : 765 – 786 .
   PubMed Web of Science ®Google Scholar
• Pearson , RK . 1999 . Discrete-time Dynamic Models , Oxford : Oxford University Press .
   Google Scholar
• Principe , JC , Rathie , A and Kuo , JM . 1992 . Prediction of chaotic time series with neural networks and the issue of dynamic modelling . International Journal of Bifurcation and Chaos , 2 : 989 – 996 .
   Google Scholar
• Soltani , S . 2002 . On the use of wavelet decomposition for time series prediction . Neurocomputing , 48 : 267 – 277 .
   Web of Science ®Google Scholar
• Sureshbabu , N and Farrell , A . 1999 . Wavelet-based system identification for non-linear control . IEEE Transactions on Automatic Control , 44 : 412 – 417 .
   Web of Science ®Google Scholar
• Tang , Z , Almeida , C and Fishwick , PA . 1991 . Time series forecasting using neural networks vs. Box-Jenkins methodology . Simulation , 57 : 303 – 310 .
   Google Scholar
• Tsatsanis , MK and Giannakis , GB . 1993 . Time-varying system identification and model validation using wavelets . IEEE Trans. Signal Processing , 41 : 3512 – 3523 .
   Web of Science ®Google Scholar
• Wei , HL and Billings , SA . 2002 . Identification of time-varying systems using multi-resolution wavelet models . International Journal of Systems Science , 33 : 1217 – 1228 .
   Web of Science ®Google Scholar
• Wei , HL and Billings , SA . 2004 . A unified wavelet-based modelling framework for non-linear system identification: the WANARX model structure . International Journal of Control , 77 : 351 – 366 .
   Web of Science ®Google Scholar
• Wei , HL , Billings , SA and Liu , J . 2004 . Term and variable selection for non-linear system identification . International Journal of Control , 77 : 86 – 110 .
   Web of Science ®Google Scholar
• Wei , HL , Billings , SA and Balikhin , MA . 2004 . Prediction of the Dst index using multiresolution wavelet models . Journal of Geophysical Research-Space Physics , 109A, A07212 : 1 – 12 .
   Google Scholar
• Weigend , AS , Huberman , BA and Rumelhart , DE . 1990 . Predicting the future: a connectionist approach . International Journal of Neural Systems , 1 : 193 – 209 .
   Google Scholar
• Weigend , AS , Huberman , BA and Rumelhart , DE . 1992 . “ Predicting sunspots and exchange rates with connectionist networks ” . In Non-linear Modelling and Forecasting , Edited by: Casdagli , M and Eubank , S . 395 – 432 . Redwood City, CA : Addison-Wesley .
   Google Scholar
• Zaldivar , JM , Gutiérrez , E , Galván , IM , Strozzi , F and Tomasin , A . 2000 . Forecasting high waters at Venice Lagoon using chaotic time series analysis and nonlinear neural networks . Journal of Hydroinformatics , 2 : 61 – 84 .
   Google Scholar
• Zhang , GQ , Patuow , BE and Hu , MY . 1998 . Forecasting with artificial neural networks: the state of the art . International Journal of Forecasting , 14 : 35 – 62 .
   Web of Science ®Google Scholar
• Zhang , Q . 1997 . “Using wavelet network in nonparametric estimation . IEEE Transactions on Neural Networks , 8 : 227 – 236 .
   PubMed Web of Science ®Google Scholar
• Zhang , Q and Benveniste , A . 1992 . Wavelet networks . IEEE Transactions on Neural Networks , 3 : 889 – 898 .
   PubMed Web of Science ®Google Scholar
• Zheng , Y , Lin , Z and Tay , DBH . 2001 . Time-varying parametric system multiresolution identification by wavelets . International Journal of Systems Science , 32 : 775 – 793 .
   Web of Science ®Google Scholar