Chaotic time series. Part I. Estimation of some invariant properties in state-space

Kugiumtzis, Dimitris; Lillekjendlie, Bjørn; Christophersen, Nils

doi:10.4173/mic.1994.4.1

Cited by 53 publications

(25 citation statements)

References 73 publications

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“…The dimension m will be found when the false nearest neighbors percentage falls below some limit, typically set to 1%, [12], and, thus, by choosing Pmax=10 and using Matlab code we finally calculate the quantity P. The so obtained results are shown in Fig. 2 indicating that the application of the FNN method yields a minimum embedding dimension m equal to 5,4,5,4,5 for Greece, Turkey,Russia,Brazil and China …”

Section: Embedding Dimension Mmentioning

confidence: 98%

Predicting the CDS return index

Hanias¹,

Magafas²,

Özün³

2011

JESTR

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This paper sets out to apply concepts of non linear dynamics theory nai neural networks to the prediction of CDS index using Greek, Turkey, Russia, Brazil and China data. The research employs the method of false near neighbors in the time series analysis in order to estimate the minimum membedding dimensions of the corresponding strange attractor. To achieve out of the sample multistep ahead prediction, a neural net is constructed which architectures based on strange attractors topological properties

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Section: Embedding Dimension Mmentioning

confidence: 98%

Predicting the CDS return index

Hanias¹,

Magafas²,

Özün³

2011

JESTR

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show abstract

“…Singular spectrum analysis (SSA) is originally designed to extract information from short noisy chaotic time series, to provide an insight to the unknown dynamics and to enhance the signal to noise ratio [34,35]. Data adaptive noise cancellation is fundamental in the analysis of natural time series, because they often have a chaotic behavior showing an inherent continuous spectrum which resembles white noise [36]. To show the advantage of this method, the performance of singular spectrum analysis and fuzzy descriptor model with its extended learning algorithm is compared with several neural and neurofuzzy models in the prediction of chaotic time series with limited number of observations.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy descriptor systems and spectral analysis for chaotic time series prediction

Mirmomeni

Lucas

Shafiee

et al. 2009

Neural Comput & Applic

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Predicting future behavior of chaotic time series and systems is a challenging area in the literature of nonlinear systems. The prediction accuracy of chaotic time series is extremely dependent on the model and the learning algorithm. In addition, the generalization property of the proposed models trained by limited observations is of great importance. In the past two decades, singular or descriptor systems and related fuzzy descriptor models have been the subjects of interest due to their many practical applications in modeling complex phenomena. In this study fuzzy descriptor models, as a more recent neurofuzzy realization of locally linear descriptor systems, which have led to the introduction of intuitive incremental learning algorithm that is called Generalized Locally Linear Model Tree algorithm, are implemented in their optimal structure to be compared with several other methods. A simple but efficient technique, based on the error indices of multiple validation sets, is used to optimize the number of neurons as well as to prevent over fitting in the incremental learning algorithms. The aim of the paper is to demonstrate the advantages of fuzzy descriptor models and to make a fair comparison between the most successful neural and neurofuzzy approaches in their best structures according to prediction accuracy, generalization, and computational complexity. The Mackey-Glass time series, Lorenz time series (as two well-known classic benchmarks), Darwin sea level pressure time series and long-term prediction of Disturbance Storm Time index, an important index of geomagnetic activity (as two natural chaotic dynamics) are used as practical examples to evaluate the power of the proposed method in long term prediction of chaotic dynamics.

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“…SSA is originally designed to extract information from short noisy chaotic time series, to provide an insight to the unknown dynamics and to enhance the signal to noise ratio [30,31]. Data adaptive noise cancellation is fundamental in the analysis of natural time series because they often have a chaotic behavior showing an inherent continuous spectrum which resembles white noise [32]. In this research, another aspect of SSA is mainly considered: SSA performs a data adaptive filtering in the lag coordinate space of data and yields the principal components (PCs) of time series which have narrow band frequency spectra and obvious temporal patterns.…”

Section: Introductionmentioning

confidence: 99%

Extracting the main patterns of natural time series for long-term neurofuzzy prediction

Gholipour

Lucas

Araabi

et al. 2006

Neural Comput & Applic

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A combination of singular spectrum analysis and locally linear neurofuzzy modeling technique is proposed to make accurate long-term prediction of natural phenomena. The principal components (PCs) obtained from spectral analysis have narrow band frequency spectra and definite linear or nonlinear trends and periodic patterns; hence they are predictable in large prediction horizon. The incremental learning algorithm initiates a model for each of the components as an optimal linear least squares estimation, and adds the nonlinear neurons if they help to reduce error indices over training and validation sets. Therefore, the algorithm automatically constructs the best linear or nonlinear model for each of the PCs to achieve maximum generalization, and the long-term prediction of the original time series is obtained by recombining the predicted components. The proposed method has been primarily tested in long-term prediction of some wellknown nonlinear time series obtained from MackeyGlass, Lorenz, and Ikeda map chaotic systems, and the results have been compared to the predictions made by multi-layered perceptron (MLP) and radial basis functions (RBF) networks. As a real world case study, the method has been applied to the long-term prediction of solar activity where the results have been compared to the long-term predictions of physical precursor and solar dynamo methods.

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Chaotic time series. Part I. Estimation of some invariant properties in state-space

Cited by 53 publications

References 73 publications

Predicting the CDS return index

Predicting the CDS return index

Fuzzy descriptor systems and spectral analysis for chaotic time series prediction

Extracting the main patterns of natural time series for long-term neurofuzzy prediction

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