IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v637y2024ics0378437124000426.html
   My bibliography  Save this article

Bridge successive states for a complex system with evolutionary matrix

Author

Listed:
  • Yan, Shuang
  • Gu, Changgui
  • Yang, Huijie

Abstract

A concept called temporal network of evolutionary matrices is proposed to identify the evolutionary laws for complex systems. The key idea is to separate the trajectory into overlapping segments. The time step between each pair of successive states is assumed to be so short that they can be bridged by a matrix. And the time duration covered by the segment is assumed to be so short that the matrices bridging the pairs of successive states are identical, called evolutionary matrix. The trajectory is them mapped to a temporal network of evolutionary matrices (“bridges”), describing the evolutionary law. Investigations on the series generated with the fractional Brownian motion, and the records for stock markets distributed over the world show that, there exist in all the evolutionary angle series long-range correlations. For the fBm increment series, the series generated with the Heston model, and stock index series, the influences of variables on themselves and the influences between adjacent variables form the backbone of the temporal networks. Non-adjacent impacts can fluctuate simultaneously. The markets in Japan as the center affects Mainland China and is unilaterally affected by the America and Mainland China. After financial crisis, there appear some abrupt and large fluctuations of the evolutionary matrices for the components of the Dow Jones stock market.

Suggested Citation

  • Yan, Shuang & Gu, Changgui & Yang, Huijie, 2024. "Bridge successive states for a complex system with evolutionary matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    • Handle: RePEc:eee:phsmap:v:637:y:2024:i:c:s0378437124000426
    DOI: 10.1016/j.physa.2024.129534
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437124000426
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2024.129534?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. Sunil Kumar & Nivedita Deo, 2012. "Correlation, Network and Multifractal Analysis of Global Financial Indices," Papers 1202.0409, arXiv.org.
    2. Christopher F. Clements & Michael A. McCarthy & Julia L. Blanchard, 2019. "Early warning signals of recovery in complex systems," Nature Communications, Nature, vol. 10(1), pages 1-9, December.
    3. Moritz Schularick & Alan M. Taylor, 2012. "Credit Booms Gone Bust: Monetary Policy, Leverage Cycles, and Financial Crises, 1870-2008," American Economic Review, American Economic Association, vol. 102(2), pages 1029-1061, April.
    4. Martin Forde & Antoine Jacquier & Aleksandar Mijatovic, 2009. "Asymptotic formulae for implied volatility in the Heston model," Papers 0911.2992, arXiv.org, revised May 2010.
    5. Li Zhou & Lu Qiu & Changgui Gu & Huijie Yang, 2018. "Immediate Causality Network of Stock Markets," Papers 1802.02699, arXiv.org.
    6. Roberto Casarin & Flaminio Squazzoni, 2013. "Being on the Field When the Game Is Still Under Way. The Financial Press and Stock Markets in Times of Crisis," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-14, July.
    7. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    8. Dong-Ming Song & Michele Tumminello & Wei-Xing Zhou & Rosario N. Mantegna, 2011. "Evolution of worldwide stock markets, correlation structure and correlation based graphs," Papers 1103.5555, arXiv.org.
    9. Yuan, Qianshun & Semba, Sherehe & Zhang, Jing & Weng, Tongfeng & Gu, Changgui & Yang, Huijie, 2021. "Multi-scale transition matrix approach to time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    10. Yuan, Qianshun & Zhang, Jing & Wang, Haiying & Gu, Changgui & Yang, Huijie, 2023. "A multi-scale transition matrix approach to chaotic time series," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    11. Amir Bashan & Ronny P. Bartsch & Jan. W. Kantelhardt & Shlomo Havlin & Plamen Ch. Ivanov, 2012. "Network physiology reveals relations between network topology and physiological function," Nature Communications, Nature, vol. 3(1), pages 1-9, January.
    12. Mutua Stephen & Changgui Gu & Huijie Yang, 2015. "Visibility Graph Based Time Series Analysis," PLOS ONE, Public Library of Science, vol. 10(11), pages 1-19, November.
    13. Wang, Xiaoyan & Han, Xiujing & Chen, Zhangyao & Bi, Qinsheng & Guan, Shuguang & Zou, Yong, 2022. "Multi-scale transition network approaches for nonlinear time series analysis," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    14. Hsiao, Cheng, 1981. "Autoregressive modelling and money-income causality detection," Journal of Monetary Economics, Elsevier, vol. 7(1), pages 85-106.
    15. Marten Scheffer & Jordi Bascompte & William A. Brock & Victor Brovkin & Stephen R. Carpenter & Vasilis Dakos & Hermann Held & Egbert H. van Nes & Max Rietkerk & George Sugihara, 2009. "Early-warning signals for critical transitions," Nature, Nature, vol. 461(7260), pages 53-59, September.
    Full references (including those not matched with items on IDEAS)

    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. Yuan, Qianshun & Zhang, Jing & Wang, Haiying & Gu, Changgui & Yang, Huijie, 2023. "A multi-scale transition matrix approach to chaotic time series," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    2. Archil Gulisashvili & Peter Laurence, 2013. "The Heston Riemannian distance function," Papers 1302.2337, arXiv.org.
    3. Nobi, Ashadun & Maeng, Seong Eun & Ha, Gyeong Gyun & Lee, Jae Woo, 2014. "Effects of global financial crisis on network structure in a local stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 135-143.
    4. Jae Woo Lee & Ashadun Nobi, 2018. "State and Network Structures of Stock Markets around the Global Financial Crisis," Papers 1806.04363, arXiv.org.
    5. Charles-Cadogan, G., 2021. "Market Instability, Investor Sentiment, And Probability Judgment Error in Index Option Prices," CRETA Online Discussion Paper Series 71, Centre for Research in Economic Theory and its Applications CRETA.
    6. Antoine Jacquier & Aleksandar Mijatović, 2014. "Large Deviations for the Extended Heston Model: The Large-Time Case," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(3), pages 263-280, September.
    7. Jae Woo Lee & Ashadun Nobi, 2018. "State and Network Structures of Stock Markets Around the Global Financial Crisis," Computational Economics, Springer;Society for Computational Economics, vol. 51(2), pages 195-210, February.
    8. Chun-Xiao Nie & Fu-Tie Song, 2021. "Entropy of Graphs in Financial Markets," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 1149-1166, April.
    9. Archil Gulisashvili & Josef Teichmann, 2014. "The G\"{a}rtner-Ellis theorem, homogenization, and affine processes," Papers 1406.3716, arXiv.org.
    10. Gautier Marti & Frank Nielsen & Miko{l}aj Bi'nkowski & Philippe Donnat, 2017. "A review of two decades of correlations, hierarchies, networks and clustering in financial markets," Papers 1703.00485, arXiv.org, revised Nov 2020.
    11. Shuaiqiang Liu & Anastasia Borovykh & Lech A. Grzelak & Cornelis W. Oosterlee, 2019. "A neural network-based framework for financial model calibration," Papers 1904.10523, arXiv.org.
    12. Li, Yan & Jiang, Xiong-Fei & Tian, Yue & Li, Sai-Ping & Zheng, Bo, 2019. "Portfolio optimization based on network topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 671-681.
    13. Leif Andersen & Alexander Lipton, 2012. "Asymptotics for Exponential Levy Processes and their Volatility Smile: Survey and New Results," Papers 1206.6787, arXiv.org.
    14. Chen, Yu & Ling, Guang & Song, Xiangxiang & Tu, Wenhui, 2023. "Characterizing the statistical complexity of nonlinear time series via ordinal pattern transition networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    15. Wang, Gang-Jin & Xie, Chi, 2015. "Correlation structure and dynamics of international real estate securities markets: A network perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 424(C), pages 176-193.
    16. Caraiani, Petre, 2014. "The predictive power of singular value decomposition entropy for stock market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 571-578.
    17. Jacquier, Antoine & Roome, Patrick, 2016. "Large-maturity regimes of the Heston forward smile," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1087-1123.
    18. Caraiani, Petre, 2017. "The predictive power of local properties of financial networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 79-90.
    19. Nobi, Ashadun & Alam, Shafiqul & Lee, Jae Woo, 2017. "Dynamic of consumer groups and response of commodity markets by principal component analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 337-344.
    20. Florence Guillaume & Wim Schoutens, 2014. "Heston Model: The Variance Swap Calibration," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 76-89, April.

    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:phsmap:v:637:y:2024:i:c:s0378437124000426. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.