On the existence of proper stochastic Markov models for statistical reconstruction and prediction of chaotic time series

Jokar, Meysam; Salarieh, Hassan; Alasty, Aria

doi:10.1016/j.chaos.2019.04.008

Cited by 8 publications

(2 citation statements)

References 19 publications

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“…Lastly, concluding remarks and current frontiers in the elaborated context are briefly to be stated. Current gaps in research and frontiers on the reconstruction of attractors is vastly seen in the application of neural network, evolutionary algorithms and other reconstruction methodologies to obtain sufficient and high-quality reconstructions and analysis insights (see [116,117]). Nonetheless, the research field of time-series reconstruction and quantification of empirical DGPs is scarce and defined as a current gap in research, particularly, in hindsight of novel technological advancements such as artificial intelligence solutions.…”

Section: Discussionmentioning

confidence: 99%

Chaos Analysis Framework: How to Safely Identify and Quantify Time-Series Dynamics

Vogl¹

2023

Nonlinear Systems - Recent Developments and Advances

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Within this chapter, a practical introduction to a nonlinear analysis framework tailored for time-series data is provided, enabling the safe quantification of underlying evolutionary dynamics, which describe the referring empirical data generating process. Furthermore, its application provides the possibility to distinct between underlying chaotic versus stochastic dynamics. In addition, an optional combination with (strange) attractor reconstruction algorithms to visualize the denoted system’s dynamics is possible. Since the framework builds upon a large variety of algorithms and methods, its application is by far trivial, especially, in hindsight of reconstruction algorithms for (strange) attractors. Therefore, a general implementation and application guideline for the correct algorithm specifications and avoidance of pitfalls or other unfavorable settings is proposed and respective (graphical) empirical examples are shown. It is intended to provide the readers the possibility to incorporate the proposed analysis framework themselves and to conduct the analyses and reconstructions properly with correct specifications and to be knowledgeable about misleading propositions or parameter choices. Finally, concluding remarks, future avenues of research and future refinements of the framework are proposed.

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Section: Discussionmentioning

confidence: 99%

Chaos Analysis Framework: How to Safely Identify and Quantify Time-Series Dynamics

Vogl¹

2023

Nonlinear Systems - Recent Developments and Advances

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“…In the 1980s, Packard, Lekscha and Donner [7], Jokar et al, [8] proposed the phase space reconstruction theory, which defines the phase space as a geometric space that determines the phase, i.e., the state of a system at a certain time. The main idea of this theory is as follows: In a dynamic system, the change of any component depends on its closely related components.…”

Section: Phase Space Reconstruction Of Chaotic Time Seriesmentioning

confidence: 99%

Prediction of Energy-Efficient Production of Coalbed Methane Based on Chaotic Time Series and Bayes-Least Squares-Support Vector Machine

Wang¹,

Man²,

Lu³

2020

IJHT

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The productivity of coalbed methane (CBM) depends heavily on the heat environment, and directly reflects the quality of the well. Following the theories of phase space reconstruction and Bayesian evidence framework, this paper puts forward a Bayes-least squares-support vector machine (Bayes-LS-SVM) model for the prediction of energy-efficient productivity of CBM under Bayesian evidence network based on chaotic time series. The energy-efficient productivity stands for the gas and water production of CBM wells at a low energy consumption, despite the disturbance from the heat environment. The proposed model avoids the local optimum trap of backpropagation neural network (BPNN), and overcomes the main defects of the SVM: high time consumption of parameter determination, and proneness to overfitting. In our model, the model parameters are optimized through three-layer Bayesian evidence inference, and the input vector for prediction is selected adaptively. In this way, the model construction is not too empirical, and the constructed model is highly adaptive. Then, the theory on phase space reconstruction was applied to investigate the chaotic property of the time series on CBM production, and the Bayes-LS-SVM was adopted to predict the time series after phase space reconstruction, in comparison with neural network prediction methods like SVM and BPNN. Experimental results show that the proposed model boast quick computing, accurate fitting, flexible structure, and strong generalization ability.

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A deep granular network with adaptive unequal-length granulation strategy for long-term time series forecasting and its industrial applications

et al. 2020

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On the existence of proper stochastic Markov models for statistical reconstruction and prediction of chaotic time series

Cited by 8 publications

References 19 publications

Chaos Analysis Framework: How to Safely Identify and Quantify Time-Series Dynamics

Chaos Analysis Framework: How to Safely Identify and Quantify Time-Series Dynamics

Prediction of Energy-Efficient Production of Coalbed Methane Based on Chaotic Time Series and Bayes-Least Squares-Support Vector Machine

A deep granular network with adaptive unequal-length granulation strategy for long-term time series forecasting and its industrial applications

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