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For the noisy chaotic series prediction problem, traditional methods are quite empirical, and are lacking in the analysis of the composition of the prediction error, thereby ignoring the the difference between chaotic dynamics reconstruction and prediction model. Based on the composition of actual prediction error, the predictor bias error and input disturbance error are defined in this paper and two kinds of global forecasts, ensemble least-square method and regularization method are analysed. It is shown that the ensemble least-square method is suitable for the reconstruction of chaotic dynamics, but has a greater influence on the predictor error. On the other hand, the regularization method can improve the sensitivity of the predictor, but it can be influenced by the input perturbation error. Two simulation examples are used to demonstrate the difference between the chaotic dynamical reconstruction and the establishment of prediction model, and to compare the ensamble least-square method and the regularization method, and at the same time indicate that the actual prediction error is influenced both by the input disturbance error and by the predictor error. In practice, a balance should be stricken between the two, in order to optimize the model prediction accuracy.
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Keywords:
- chaotic time series prediciton /
- noise /
- ensemble least square /
- regularization
[1] Karunasinghe D S K, Liong S Y 2006 J. Hydrol. 323 1
[2] Zhao P, Xing L, Yu J 2009 Phys. Lett. A 373 25
[3] Molkov Y I, Mukhin D N, Loskutov E M, Timushev R I, Feigin A M 2011 Phys. Rev. E 84 3
[4] Leung H, Lo T, Wang S 2001 IEEE Trans. Neural Netw. 12 5
[5] Chen D Y, Liu Y, Ma X Y 2012 Acta Phys. Sin. 61 10 (in Chinese) [陈帝伊, 柳烨, 马孝义 2012 物理学报 61 10]
[6] Su L 2010 Compu. Math. Appl. 59 2
[7] Jaeger H, Haas H 2004 Science 304 5667
[8] Song Q S, Feng Z R, Li R H 2009 Acta Phys. Sin. 58 7 (in Chinese) [宋青松, 冯祖仁, 李人厚 2009 物理学报 58 7]
[9] Li D C, Han M, Wang J 2012 IEEE Trans. Neural Netw. Learn. Syst. 23 5
[10] Zhang J F, Hu S S 2008 Acta Phys. Sin. 57 5 (in Chinese) [张军峰, 胡寿松 2008 物理学报 57 5]
[11] Lau K, Wu Q 2008 Pattern Recognit. 41 5
[12] Shi Z W, Han M 2007 IEEE Trans. Neural Netw. 18 2
[13] Gu H, Wang H 2007 Appl. Math. Comput. 185 2
[14] Gao J B, Sultan H, Hu J, Tung W W 2010 IEEE Signal Process. Lett. 17 3
[15] Gan J C, Xiao X C 2004 Chin. Phys. 13 3
[16] Feng J C 2005 Chin. Phys. Lett. 22 8
[17] Zhang J S, Xiao X C 2000 Chin. Phys. 9 6
[18] Van G J, Schoukens J, Pintelon R 2000 IEEE Trans. Neural Netw. 11 2
[19] Lee C C, Chiang Y C, Shih C Y, Tsai C L 2009 Expert Syst. Appl. 36 3
[20] Lei M, Meng G 2008 Chaos Solitons Fract. 36 2
[21] Bishop C M 1995 Neural Comput. 7 1
[22] An G Z 1996 Neural Comput. 8 3
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[1] Karunasinghe D S K, Liong S Y 2006 J. Hydrol. 323 1
[2] Zhao P, Xing L, Yu J 2009 Phys. Lett. A 373 25
[3] Molkov Y I, Mukhin D N, Loskutov E M, Timushev R I, Feigin A M 2011 Phys. Rev. E 84 3
[4] Leung H, Lo T, Wang S 2001 IEEE Trans. Neural Netw. 12 5
[5] Chen D Y, Liu Y, Ma X Y 2012 Acta Phys. Sin. 61 10 (in Chinese) [陈帝伊, 柳烨, 马孝义 2012 物理学报 61 10]
[6] Su L 2010 Compu. Math. Appl. 59 2
[7] Jaeger H, Haas H 2004 Science 304 5667
[8] Song Q S, Feng Z R, Li R H 2009 Acta Phys. Sin. 58 7 (in Chinese) [宋青松, 冯祖仁, 李人厚 2009 物理学报 58 7]
[9] Li D C, Han M, Wang J 2012 IEEE Trans. Neural Netw. Learn. Syst. 23 5
[10] Zhang J F, Hu S S 2008 Acta Phys. Sin. 57 5 (in Chinese) [张军峰, 胡寿松 2008 物理学报 57 5]
[11] Lau K, Wu Q 2008 Pattern Recognit. 41 5
[12] Shi Z W, Han M 2007 IEEE Trans. Neural Netw. 18 2
[13] Gu H, Wang H 2007 Appl. Math. Comput. 185 2
[14] Gao J B, Sultan H, Hu J, Tung W W 2010 IEEE Signal Process. Lett. 17 3
[15] Gan J C, Xiao X C 2004 Chin. Phys. 13 3
[16] Feng J C 2005 Chin. Phys. Lett. 22 8
[17] Zhang J S, Xiao X C 2000 Chin. Phys. 9 6
[18] Van G J, Schoukens J, Pintelon R 2000 IEEE Trans. Neural Netw. 11 2
[19] Lee C C, Chiang Y C, Shih C Y, Tsai C L 2009 Expert Syst. Appl. 36 3
[20] Lei M, Meng G 2008 Chaos Solitons Fract. 36 2
[21] Bishop C M 1995 Neural Comput. 7 1
[22] An G Z 1996 Neural Comput. 8 3
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