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 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.

[1]  Lixin Tian,et al.  Chaotic characteristic identification for carbon price and an multi-layer perceptron network prediction model , 2015, Expert Syst. Appl..

[2]  Eric Huang,et al.  Real-time multi-step-ahead water level forecasting by recurrent neural networks for urban flood control , 2014 .

[3]  Jingwei Song,et al.  A Multistep Chaotic Model for Municipal Solid Waste Generation Prediction. , 2014, Environmental engineering science.

[4]  Li Shi-yin,et al.  Short-Term Forecasting Method of Coalmine Gas Concentration Based on Chaotic Time Series , 2008 .

[5]  I. Soto,et al.  Project-Based Learning versus Cooperative Learning courses in Engineering Students , 2015, IEEE Latin America Transactions.

[6]  Lei Dong,et al.  Ultra-short-term Wind Power Prediction based on Chaos Phase Space Reconstruction and NWP , 2015 .

[7]  Shibing Zhang,et al.  L-PLC Channel Characteristics Prediction Based on SVM , 2008, 2008 IEEE International Conference on Networking, Sensing and Control.

[8]  Han Xiao,et al.  Parameters identification of chaotic system by chaotic gravitational search algorithm , 2012, Chaos, Solitons & Fractals.

[9]  Dimitrios Alexios Karras,et al.  Efficient Multistep Nonlinear Time Series Prediction involving Deterministic Chaos based Local Reconstruction methodologies and Multi-layer Perceptron Neural Networks in Diode Resonator Circuits , 2016 .

[10]  Robert Jenssen,et al.  Recurrent Neural Networks for Short-Term Load Forecasting , 2017, SpringerBriefs in Computer Science.

[11]  Ismael Soto,et al.  Chaotic Time Series for Copper's Price Forecast - Neural Networks and the Discovery of Knowledge for Big Data , 2018, ICISO.

[12]  Zhongyi Hu,et al.  Multi-step-ahead time series prediction using multiple-output support vector regression , 2014, Neurocomputing.

[13]  G. Fuertes,et al.  Predictive analysis of energy consumption in minining for making decisions , 2018, 2018 7th International Conference on Computers Communications and Control (ICCCC).

[14]  M. Siek,et al.  Nonlinear Processes in Geophysics Nonlinear chaotic model for predicting storm surges , 2022 .

[15]  S. N. Rasband,et al.  Chaotic Dynamics of Nonlinear Systems , 1990 .

[16]  Elena Grigorenko,et al.  Chaotic dynamics of the fractional Lorenz system. , 2003, Physical review letters.

[17]  Kunikazu Kobayashi,et al.  Time series forecasting using a deep belief network with restricted Boltzmann machines , 2014, Neurocomputing.

[18]  Shu Gong,et al.  Prediction of Wind Power by Chaos and BP Artificial Neural Networks Approach Based on Genetic Algorithm , 2015 .

[19]  Antje Sommer.  Nonlinear Dynamical Economics And Chaotic Motion , 2016 .

[20]  Joshua Garland,et al.  Prediction in projection. , 2015, Chaos.

[21]  Guillermo Fuertes Sanchez,et al.  Project-Based Learning versus Cooperative Learning courses in Engineering Students , 2015 .

[22]  Miguel Alfaro,et al.  Proposal of Two Measures of Complexity Based on Lempel-Ziv for Dynamic Systems: An Application for Manufacturing Systems , 2018 .

[23]  Miguel Alfaro,et al.  The Effect of Entropy on the Performance of Modified Genetic Algorithm Using Earthquake and Wind Time Series , 2018, Complex..

[24]  M. G. De Giorgi,et al.  Comparison of strategies for multi-step ahead photovoltaic power forecasting models based on hybrid group method of data handling networks and least square support vector machine , 2016 .

[25]  R. Carrasco,et al.  Copper Metal Price Using Chaotic Time Series Forecating , 2015, IEEE Latin America Transactions.

[26]  Ozgur Kisi,et al.  Modelling daily dissolved oxygen concentration using least square support vector machine, multivariate adaptive regression splines and M5 model tree , 2018 .

[27]  Jian Xi Yang,et al.  Prediction of Chaotic Time Series of Bridge Monitoring System Based on Multi-Step Recursive BP Neural Network , 2010 .

[28]  Miguel Alfaro,et al.  Forecasting Chaotic Series in Manufacturing Systems by Vector Support Machine Regression and Neural Networks , 2012, Int. J. Comput. Commun. Control.