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

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  • Jokar, Meysam
  • Salarieh, Hassan
  • Alasty, Aria

Abstract

In this paper, the problem of statistical reconstruction and prediction of chaotic systems with unknown governing equations using stochastic Markov models is investigated. Using the time series of only one measurable state, an algorithm is proposed to design any orders of Markov models and the approach is state transition matrix extraction. Using this modeling, two goals are followed: first, using the time series, statistical reconstruction is performed through which the probability density and conditional probability density functions are reconstructed; and second, prediction is performed. For this problem, some estimators are required and here the maximum likelihood and the conditional expected value are used. The efficiency of this algorithm has been investigated by applying it to some typical data. To illustrate the advantages of this model, a deterministic model based on the nearest neighbors in the delayed phase space is used. It will be seen that using the appropriate Markov model order and sufficient number of meshes, the proposed algorithm, unlike the deterministic model, is capable of reconstructing and predicting the chaotic data in a many steps.

Suggested Citation

  • Jokar, Meysam & Salarieh, Hassan & Alasty, Aria, 2019. "On the existence of proper stochastic Markov models for statistical reconstruction and prediction of chaotic time series," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 373-382.
    • Handle: RePEc:eee:chsofr:v:123:y:2019:i:c:p:373-382
    DOI: 10.1016/j.chaos.2019.04.008
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    References listed on IDEAS

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    1. Kaveh, H. & Salarieh, H. & Hajiloo, R., 2018. "On the control of unknown continuous time chaotic systems by applying Takens embedding theory," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 53-57.
    2. Wai-Ki Ching & Michael K. Ng, 2006. "Markov Chains: Models, Algorithms and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-29337-0, December.
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    Cited by:

    1. Kaveh, Hojjat & Salarieh, Hassan, 2020. "A new approach to extreme event prediction and mitigation via Markov-model-based chaos control," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).

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