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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, M
; Sharif University of Technology
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2019

328
Viewed

- Type of Document: Article
- DOI: 10.1016/j.chaos.2019.04.008
- Publisher: Elsevier Ltd , 2019
- 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. © 2019 Elsevier Ltd
- Keywords:
- Chaotic time series ; Deterministic model of nearest neighbors ; Markov modeling ; Prediction ; Statistical reconstruction ; Chaotic systems ; Forecasting ; Markov processes ; Maximum likelihood ; Probability density function ; Stochastic systems ; Time series ; Conditional probability density ; Deterministic modeling ; Markov model ; Nearest neighbors ; Probability densities ; State transition Matrix ; Stochastic models
- Source: Chaos, Solitons and Fractals ; Volume 123 , 2019 , Pages 373-382 ; 09600779 (ISSN)
- URL: https://www.sciencedirect.com/science/article/abs/pii/S0960077919301183