IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v123y2019icp373-382.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077919301183
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.04.008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Villacorta, Pablo J. & Verdegay, José L., 2016. "FuzzyStatProb: An R Package for the Estimation of Fuzzy Stationary Probabilities from a Sequence of Observations of an Unknown Markov Chain," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 71(i08).
    2. Fokianos, Konstantinos & Fried, Roland & Kharin, Yuriy & Voloshko, Valeriy, 2022. "Statistical analysis of multivariate discrete-valued time series," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. Alicja Ganczarek-Gamrot & Józef Stawicki, 2017. "Comparison of certain dynamic estimation methods of Value at Risk on Polish gas market," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 17, pages 81-96.
    4. Suryadeepto Nag & Sankarshan Basu & Siddhartha P. Chakrabarty, 2022. "Modeling the Commodity Prices of Base Metals in Indian Commodity Market Using a Higher Order Markovian Approach," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 159-171, March.
    5. Joseph Gogodze, 2021. "Ranking Demographic Conditions: MCDM Approach," SN Operations Research Forum, Springer, vol. 2(2), pages 1-12, June.
    6. Perkin, Joshuah S. & Gido, Keith B. & Al-Ta’ani, Ola & Scoglio, Caterina, 2013. "Simulating fish dispersal in stream networks fragmented by multiple road crossings," Ecological Modelling, Elsevier, vol. 257(C), pages 44-56.
    7. 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).
    8. João Nicolau & Flavio Riedlinger, 2015. "Estimation and inference in multivariate Markov chains," Statistical Papers, Springer, vol. 56(4), pages 1163-1173, November.
    9. Józef Stawicki, 2016. "Using the First Passage Times in Markov Chain model to support financial decisions on the stock exchange," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 16, pages 37-47.
    10. Dong-Mei Zhu & Wai-Ki Ching & Robert J. Elliott & Tak-Kuen Siu & Lianmin Zhang, 2017. "A Higher-order interactive hidden Markov model and its applications," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(4), pages 1055-1069, October.
    11. Edward Sandoyan & David Manukyan, 2013. "Exchange Rate Forecast: a New Approach for Armenian Dram," Transition Studies Review, Springer;Central Eastern European University Network (CEEUN), vol. 20(2), pages 159-177, October.
    12. Otero, Dino & Galetti, Diógenes & Mizrahi, Salomon S., 2018. "Modeling vehicular traffic networks. Part I," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 97-110.
    13. Luis R. Izquierdo & Segismundo S. Izquierdo & José Manuel Galán & José Ignacio Santos, 2009. "Techniques to Understand Computer Simulations: Markov Chain Analysis," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 12(1), pages 1-6.
    14. Michael K. Ng & Yuho Chung, 2012. "Double Mover–Stayer model on customer switching in telecommunications industry," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(8), pages 663-674, December.
    15. Bruno Damásio & João Nicolau, 2020. "Time Inhomogeneous Multivariate Markov Chains: Detecting and Testing Multiple Structural Breaks Occurring at Unknown," Working Papers REM 2020/0136, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    16. Babak Omidvar & Mohammad Hojjati Malekshah & Hamed Omidvar, 2014. "Failure risk assessment of interdependent infrastructures against earthquake, a Petri net approach: case study—power and water distribution networks," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 71(3), pages 1971-1993, April.
    17. Peter Sendfeld, 2008. "Two Queues with Weighted One-Way Overflow," Methodology and Computing in Applied Probability, Springer, vol. 10(4), pages 531-555, December.
    18. Fan, Zhenyi & Zhang, Chenkai & Wang, Yiming & Du, Baoxiang, 2023. "Construction, dynamic analysis and DSP implementation of a novel 3D discrete memristive hyperchaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:123:y:2019:i:c:p:373-382. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.