Forecast of Chaotic Series in a Horizon Superior to the Inverse of the Maximum Lyapunov Exponent
In this article, two models of the forecast of time series obtained from the chaotic dynamic systems are presented: the Lorenz system, the manufacture system, and the volume of the Great Salt Lake of Utah. The theory of the nonlinear dynamic systems indicates the capacity of making good-quality pred...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2018/1452683 |
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| author | Miguel Alfaro Guillermo Fuertes Manuel Vargas Juan Sepúlveda Matias Veloso-Poblete |
| author_facet | Miguel Alfaro Guillermo Fuertes Manuel Vargas Juan Sepúlveda Matias Veloso-Poblete |
| author_sort | Miguel Alfaro |
| collection | DOAJ |
| description | In this article, two models of the forecast of time series obtained from the chaotic dynamic systems are presented: the Lorenz system, the manufacture system, and the volume of the Great Salt Lake of Utah. The theory of the nonlinear dynamic systems indicates the capacity of making good-quality predictions of series coming from dynamic systems with chaotic behavior up to a temporal horizon determined by the inverse of the major Lyapunov exponent. The analysis of the Fourier power spectrum and the calculation of the maximum Lyapunov exponent allow confirming the origin of the series from a chaotic dynamic system. The delay time and the global dimension are employed as parameters in the models of forecast of artificial neuronal networks (ANN) and support vector machine (SVM). This research demonstrates how forecast models built with ANN and SVM have the capacity of making forecasts of good quality, in a superior temporal horizon at the determined interval by the inverse of the maximum Lyapunov exponent or theoretical forecast frontier before deteriorating exponentially. |
| format | Article |
| id | doaj-art-da6768cb94244002b08dc950a99400c6 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-da6768cb94244002b08dc950a99400c62025-02-03T06:01:32ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/14526831452683Forecast of Chaotic Series in a Horizon Superior to the Inverse of the Maximum Lyapunov ExponentMiguel Alfaro0Guillermo Fuertes1Manuel Vargas2Juan Sepúlveda3Matias Veloso-Poblete4Industrial Engineering Department, University of Santiago de Chile, Avenida Ecuador 3769, Santiago de Chile, ChileUniversidad de San Buenaventura, ColombiaFacultad de Ingeniería y Tecnología, Universidad San Sebastian, Bellavista 7, Santiago de Chile, ChileIndustrial Engineering Department, University of Santiago de Chile, Avenida Ecuador 3769, Santiago de Chile, ChileIndustrial Engineering Department, University of Santiago de Chile, Avenida Ecuador 3769, Santiago de Chile, ChileIn this article, two models of the forecast of time series obtained from the chaotic dynamic systems are presented: the Lorenz system, the manufacture system, and the volume of the Great Salt Lake of Utah. The theory of the nonlinear dynamic systems indicates the capacity of making good-quality predictions of series coming from dynamic systems with chaotic behavior up to a temporal horizon determined by the inverse of the major Lyapunov exponent. The analysis of the Fourier power spectrum and the calculation of the maximum Lyapunov exponent allow confirming the origin of the series from a chaotic dynamic system. The delay time and the global dimension are employed as parameters in the models of forecast of artificial neuronal networks (ANN) and support vector machine (SVM). This research demonstrates how forecast models built with ANN and SVM have the capacity of making forecasts of good quality, in a superior temporal horizon at the determined interval by the inverse of the maximum Lyapunov exponent or theoretical forecast frontier before deteriorating exponentially.http://dx.doi.org/10.1155/2018/1452683 |
| spellingShingle | Miguel Alfaro Guillermo Fuertes Manuel Vargas Juan Sepúlveda Matias Veloso-Poblete Forecast of Chaotic Series in a Horizon Superior to the Inverse of the Maximum Lyapunov Exponent Complexity |
| title | Forecast of Chaotic Series in a Horizon Superior to the Inverse of the Maximum Lyapunov Exponent |
| title_full | Forecast of Chaotic Series in a Horizon Superior to the Inverse of the Maximum Lyapunov Exponent |
| title_fullStr | Forecast of Chaotic Series in a Horizon Superior to the Inverse of the Maximum Lyapunov Exponent |
| title_full_unstemmed | Forecast of Chaotic Series in a Horizon Superior to the Inverse of the Maximum Lyapunov Exponent |
| title_short | Forecast of Chaotic Series in a Horizon Superior to the Inverse of the Maximum Lyapunov Exponent |
| title_sort | forecast of chaotic series in a horizon superior to the inverse of the maximum lyapunov exponent |
| url | http://dx.doi.org/10.1155/2018/1452683 |
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