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Considering the problem that simply modifying the reservoir algorithm cannot significantly improve the prediction accuracy of chaotic multivariate time series, in this paper we propose a hybrid prediction model based on error correction. The observed data includes both linear and nonlinear features. First, we use autoregressive and moving average model to capture the linear features, then build a regularized echo state network to portray the dynamic nonlinear features. Finally, we add the predicted nonlinear value to the predicted linear value, in order to improve forecasting accuracy achieved by either of the models used separately. The experimental results of Lorenz and Sunspot-Runoff in the Yellow River time series demonstrate the effectiveness and characteristics of the proposed model herein.
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Keywords:
- echo state network /
- chaos /
- multivariate time series prediction /
- error correction
[1] Xiu C B, Xu M 2010 Acta Phys. Sin. 59 7650 (in Chinese) [修春波, 徐勐 2010 物理学报 59 7650]
[2] Zhang J S, Xiao X C 2000 Acta Phys. Sin. 49 403 (in Chinese) [张家树, 肖先赐 2000 物理学报 49 403]
[3] Rojas I, Valenzuela O, Rojas F, Guillen A, Herrera L J, Pomares H, Marquez L, Pasadas M 2008 Neurocomputing 71 519
[4] Chattopadhyay S, Jhajharia D, Chattopadhyay G 2011 C. R. Geosci. 343 433
[5] Cao F L, Xu Z B 2004 Sci. China E 34 361 (in Chinese) [曹飞龙, 徐宗本 2004 中国科学: E辑 34 361]
[6] Buonomano D V 2009 Neuron 63 423
[7] Ma Q L, Zheng Q L, Peng H, Qin J W 2009 Acta Phys. Sin. 58 1410 (in Chinese) [马千里, 郑启伦, 彭宏, 覃姜维 2009 物理学报 58 1410]
[8] Zhang X, Wang H L 2011 Acta Phys. Sin. 60 110201 (in Chinese) [张弦, 王宏力 2011 物理学报 60 110201]
[9] Jaeger H, Haas H 2004 Science 304 78
[10] Song Q S, Feng Z R, Li R H 2009 Acta Phys. Sin. 58 5057 (in Chinese) [宋青松, 冯祖仁, 李人厚 2009 物理学报 58 5057]
[11] Dutoit X, Schrauwen B, Campenhout J V, Stroobandt D, Brussel H V, Nuttin M 2009 Neurocomputing 72 1534
[12] Zhang G P 2003 Neurocomputing 50 159
[13] Seghouane A K 2011 IEEE Trans. Aerosp. Electron. Syst. 47 1154
[14] Shi Z W, Han M 2007 IEEE Trans. Neural Netw. 18 359
[15] Chatzis S P, Demiris Y 2011 IEEE Trans. Neural Netw. 22 1435
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[1] Xiu C B, Xu M 2010 Acta Phys. Sin. 59 7650 (in Chinese) [修春波, 徐勐 2010 物理学报 59 7650]
[2] Zhang J S, Xiao X C 2000 Acta Phys. Sin. 49 403 (in Chinese) [张家树, 肖先赐 2000 物理学报 49 403]
[3] Rojas I, Valenzuela O, Rojas F, Guillen A, Herrera L J, Pomares H, Marquez L, Pasadas M 2008 Neurocomputing 71 519
[4] Chattopadhyay S, Jhajharia D, Chattopadhyay G 2011 C. R. Geosci. 343 433
[5] Cao F L, Xu Z B 2004 Sci. China E 34 361 (in Chinese) [曹飞龙, 徐宗本 2004 中国科学: E辑 34 361]
[6] Buonomano D V 2009 Neuron 63 423
[7] Ma Q L, Zheng Q L, Peng H, Qin J W 2009 Acta Phys. Sin. 58 1410 (in Chinese) [马千里, 郑启伦, 彭宏, 覃姜维 2009 物理学报 58 1410]
[8] Zhang X, Wang H L 2011 Acta Phys. Sin. 60 110201 (in Chinese) [张弦, 王宏力 2011 物理学报 60 110201]
[9] Jaeger H, Haas H 2004 Science 304 78
[10] Song Q S, Feng Z R, Li R H 2009 Acta Phys. Sin. 58 5057 (in Chinese) [宋青松, 冯祖仁, 李人厚 2009 物理学报 58 5057]
[11] Dutoit X, Schrauwen B, Campenhout J V, Stroobandt D, Brussel H V, Nuttin M 2009 Neurocomputing 72 1534
[12] Zhang G P 2003 Neurocomputing 50 159
[13] Seghouane A K 2011 IEEE Trans. Aerosp. Electron. Syst. 47 1154
[14] Shi Z W, Han M 2007 IEEE Trans. Neural Netw. 18 359
[15] Chatzis S P, Demiris Y 2011 IEEE Trans. Neural Netw. 22 1435
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