Open AccessLocal higher-order Volterra filter multi-step prediction model of chaotic time series
Author(s) -
Jian Du,
Yijia Cao,
Zhijian Liu,
Lizhong Xu,
Quanyuan Jiang,
Guo Chuangxin,
Lu Jin-Gui
Publication year - 2009
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.58.5997
Subject(s) - chaotic , computer science , series (stratigraphy) , phase space , filter (signal processing) , nonlinear system , similarity (geometry) , volterra series , euclidean distance , euclidean space , set (abstract data type) , algorithm , mathematics , control theory (sociology) , artificial intelligence , mathematical analysis , image (mathematics) , physics , paleontology , control (management) , quantum mechanics , computer vision , biology , programming language , thermodynamics
In general, the prediction modeling of chaotic time series is conducted by Volterra filters through constructing nonlinear fitting functions according to the methodology of pattern training. Since the proposed approach is consistent with the nonlinear characteristics of chaotic systems, the corresponding model turns to be more effective than conventional models. However, something abnormal is likely to occur, such as inadequate trainingor, over training, and the training data set size is not easy to choose, because the existing Volterra filters are trained point by point along the chaotic orbit. Based on the similarity of the evolving tendency of neighbor orbits in phase space, the chaotic time series multi-step-prediction model MSP-HONFIR employing the adaptive higher-order nonlinear Volterra filter HONFIR is constructed in this paper. A new method of choosing neighbor orbits in phase space is presented by considering the Euclidean distance and the evolving tendency. In addition, the criterion for the choice of the training data set size is discussed. Numerical experiments demonstrate that the performances of multi-step-prediction are improved compared to the original HONFIR method.