Practical numerical algorithms for chaotic systems
Practical numerical algorithms for chaotic systems
Recurrent neural networks and time series prediction
Recurrent neural networks and time series prediction
The roots of backpropagation: from ordered derivatives to neural networks and political forecasting
The roots of backpropagation: from ordered derivatives to neural networks and political forecasting
Physica D
Multi-step Learning Rule for Recurrent Neural Models: An Application to Time Series Forecasting
Neural Processing Letters
Neural and Adaptive Systems: Fundamentals through Simulations with CD-ROM
Neural and Adaptive Systems: Fundamentals through Simulations with CD-ROM
Recurrent Neural Networks for Prediction: Learning Algorithms,Architectures and Stability
Recurrent Neural Networks for Prediction: Learning Algorithms,Architectures and Stability
Single-Step Prediction of Chaotic Time Series Using Wavelet-Networks
CERMA '06 Proceedings of the Electronics, Robotics and Automotive Mechanics Conference - Volume 01
Time series prediction using support vector machines: a survey
IEEE Computational Intelligence Magazine
ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part III
Characterizing chaos through Lyapunov metrics
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Multiresolution FIR neural-network-based learning algorithm applied to network traffic prediction
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Incorporation of a Regularization Term to Control Negative Correlation in Mixture of Experts
Neural Processing Letters
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The accuracy of a model to forecast a time series diminishes as the prediction horizon increases, in particular when the prediction is carried out recursively. Such decay is faster when the model is built using data generated by highly dynamic or chaotic systems. This paper presents a topology and training scheme for a novel artificial neural network, named "Hybrid-connected Complex Neural Network" (HCNN), which is able to capture the dynamics embedded in chaotic time series and to predict long horizons of such series. HCNN is composed of small recurrent neural networks, inserted in a structure made of feed-forward and recurrent connections and trained in several stages using the algorithm back-propagation through time (BPTT). In experiments using a Mackey-Glass time series and an electrocardiogram (ECG) as training signals, HCNN was able to output stable chaotic signals, oscillating for periods as long as four times the size of the training signals. The largest local Lyapunov Exponent (LE) of predicted signals was positive (an evidence of chaos), and similar to the LE calculated over the training signals. The magnitudes of peaks in the ECG signal were not accurately predicted, but the predicted signal was similar to the ECG in the rest of its structure.