Stability analysis of RBF network-based state-dependent autoregressive model for nonlinear time series

Applied Soft Computing Journal

Volumn 12, Issue 1, 2012, Pages 174-181

  Gan, Min ^a,b   Peng, Hui ^a  

^a CENTRAL SOUTH UNIVERSITY   (China)

^b HEFEI UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Canadian lynx data; Limit cycle; Radial basis function network; Stability analysis; State dependent autoregressive model; Time series prediction

Indexed keywords

LIMIT CYCLE; LYNX DATA; RADIAL BASIS FUNCTIONS; STABILITY ANALYSIS; STATE-DEPENDENT; TIME SERIES PREDICTION;

COMPUTER SIMULATION; FORECASTING; PARAMETER ESTIMATION; TIME SERIES; TIME SERIES ANALYSIS;

RADIAL BASIS FUNCTION NETWORKS;

EID: 81155123024     PISSN: 15684946     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.asoc.2011.08.055     Document Type: Article

References (43)

1. Z. Cai, J. Fan, and Q. Yao Functional-coefficient regression models for nonlinear time series Journal of the American Statistical Association 95 451 2000 941 956
2. R. Chen, and L.-M. Liu Functional coefficient autoregressive models: estimation and tests of hypotheses Journal of Time Series Analysis 22 2 2001 151 173 (Pubitemid 33595905)
3. J.Z. Huang, and H. Shen Functional coefficient regression models for nonlinear time series: a polynomial spline approach Scandinavian Journal of Statistics 31 2004 515 534 (Pubitemid 39636946)
4. J.L. Harvill, and B.K. Ray Functional coefficient autoregressive models for vector time series Computational Statistics & Data Analysis 50 2006 3547 3566 (Pubitemid 43794953)
5. B.M. Akesson, and H.T. Toivonen State-dependent parameter modelling and identification of stochastic non-linear sampled-data systems Journal of Process Control 16 2006 877 886 (Pubitemid 44067445)
6. R. Zhang Proportional functional coefficient time series models Journal of Statistical Planning and Inference 139 2009 749 763
7. Z. Cai, Q. Li, and J.Y. Park Functional-coefficient models for nonstationary time series data Journal of Econometrics 148 2009 101 113
8. Y. Cao, H. Lin, T.Z. Wu, and Y. Yu Penalized spline estimation for functional coefficient regression models Computational Statistics and Data Analysis 54 2010 891 905
9. M.B. Priestley State-dependent models: a general approach to non-linear time series analysis Journal of Time Series Analysis 1 1 1980 57 71
10. C.W.J. Granger, and A.P. Andersen An Introduction to Bilinear Time Series Models 1978 Vandenhoek and Ruprecht Gottingen
11. H. Tong Threshold Models in Nonlinear Time Series Analysis 1983 Springer Verlag New York
12. T. Ozaki Non-linear time series models for non-linear random vibrations Journal of Applied Probability 17 1980 84 93
13. V. Haggan, and T. Ozaki Modeling nonlinear random vibrations using an amplitude-dependent autoregressive time series model Biometrika 68 1981 189 196
14. R. Chen, and R.S. Tsay Functional-coefficient autoregressive models Journal of the American Statistical Association 88 421 1993 298 308
15. A. Jain, and A.M. Kumar Hybrid neural network models for hydrologic time series forecasting Applied Soft Computing 7 2 2007 585 592 (Pubitemid 46205467)
16. C. Lee, Y. Chiang, C. Shih, and C. Tsai Noisy time series prediction using M-estimator based robust radial basis function neural networks with growing and pruning techniques Expert Systems with Applications 36 3 2009 4717 4724
17. F.A. Guerra, and L. dos S. Coelho Multi-step ahead nonlinear identification of Lorenz's chaotic system using radial basis neural network with learning by clustering and particle swarm optimization Chaos, Solitons & Fractals 35 5 2008 967 979 (Pubitemid 47562758)
18. L. dos S. Coelho, R.Z. Freire, G.H. dos Santos, and N. Mendes Identification of temperature and moisture content fields using a combined neural network and clustering method approach International Communications in Heat and Mass Transfer 36 4 2009 304 313
19. C. Lee, and C. Ko Time series prediction using RBF neural networks with a nonlinear time-varying evolution PSO algorithm Neurocomputing 73 1-3 2009 449 460
20. M. Gan, and H. Peng A hybrid approach for parameter optimization of RBF-AR model Proceedings of 49th IEEE Conference on Decision and Control (CDC2010) Atlanta, GA, USA 2010 December 4423 4428
21. M. Gan, H. Peng, and X. Peng A locally linear RBF network-based state-dependent AR model for nonlinear time series modeling Information Sciences 180 22 2010 4370 4383
22. P.P. Balestrassi, E. Popova, A.P. Paiva, and J.W. Marangon Lima Design of experiments on neural network's training for nonlinear time series forecasting Neurocomputing 72 4-6 2009 1160 1178
23. J. Vesin An amplitude-dependent autoregressive signal model based on a radial basis function expansion Proceedings of International Conference on Acoustics Speech, Signal Processing 3 1993 I29 I132
24. Z. Shi, Y. Tamura, and T. Ozaki Nonlinear time series modeling with the radial basis function-based state-dependent autoregressive model International Journal of System Science 30 1999 717 727
25. T. Ozaki, J.C. Jimenez, H. Peng, and V.H. Ozaki The innovation approach to the identification of nonlinear causal models in time series analysis D.R. Brillinger, E.A. Robinson, F.P. Schoenberg, Time Series Analysis and Applications to Geophysical Systems 2004 Springer New York pp. 195-226
26. H. Peng, T. Ozaki, V. Haggan-Ozaki, and Y. Toyoda A parameter optimization method for radial basis function type models IEEE Transactions on Neural Networks 14 2003 432 438
27. x decomposition process Control Engineering Practice 12 2004 191 203 (Pubitemid 38098435)
28. H. Peng, Z.J. Yang, W. Gui, and M. Wu Nonlinear system modeling and robust predictive control based on RBF-ARX model Engineering Applications of Artificial Intelligence 20 2007 1 9 (Pubitemid 44692468)
29. H. Peng, K. Nakano, and H. Shioya Nonlinear predictive control using neural nets-based local linearization ARX Model - stability and industrial application IEEE Transactions on Control Systems Technology 15 1 2007 130 143 (Pubitemid 46061030)
30. H. Peng, J. Wu, G. Inoussa, Q. Deng, and K. Nakano Nonlinear system modeling and predictive control using the RBF nets-based quasi-linear ARX model Control Engineering Practice 17 2009 59 66
31. V. Haggan-Ozaki, T. Ozaki, and Y. Toyoda An Akaike state-space controller for RBF-ARX models, IEEE Trans Control Systems Technology 17 1 2009 191 198
32. G.P. Zhang Time series forecasting using a hybrid ARIMA and neural network model Neurocomputing 50 2003 159 175 (Pubitemid 36124139)
33. Y. Katijani, W.K. Hipel, and A.L. Mcleod Forecasting nonlinear time series with feedforward neural networks: a case study of Canadian lynx data Journal of Forecasting 24 2005 105 117
34. C.H. Aladag, E. Egrioglu, and C. Kadilar Forecasting nonlinear time series with a hybrid methodology Applied Mathematics Letters 22 2009 1467 1470
35. H.Z. An, and F.C. Huang The geometrical ergodicity of nonlinear autoregressive models Statistica Sinica 6 1996 943 956
36. K.S. Chan, and H. Tong On the use of the deterministic Lyapunov function for the ergodicity of stochastic difference equations Advances in Applied Probability 17 1985 666 678
37. R.L. Tweedie Criteria for classifying general Markov chains Advances in Applied Probability 8 1975 737 771
38. D. Tjøstheim Non-linear time series and Markov chains Advances in Applied Probability 22 1990 587 611
39. D. Marquardt An algorithm for least-squares estimation of nonlinear parameters Journal of the Society for Industrial and Applied Mathematics 11 1963 431 441
40. S. Konishi, and G. Kitagawa Information Criteria and Statistical Modeling 2008 Springer Berlin
41. N.R. Swanson, and H. White A model selection approach to assessing the information in the term structure using linear models and artificial neural networks Journal of Business and Economic Statistics 13 3 1995 265 275
42. M.J.L. Orr, Introduction to radial basis function networks, 1996. available: http://www.anc.ed.ac.uk/∼mjo/rbf.html.
43. P.D. McNeis Neural Networks in Finance: Gaining Predictive Edge in the Market 2005 Elsevier Academic Press Burlington, MA