IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v34y2007i2p509-518.html
   My bibliography  Save this article

Enhanced box and prism assisted algorithms for computing the correlation dimension

Author

Listed:
  • Bueno-Orovio, Alfonso
  • Pérez-García, Víctor M.

Abstract

Box-assisted and prism-assisted algorithms are among the most popular algorithms for the computation of the correlation dimension. However, the box size is usually determined by authors just through rough estimates or even by trial and error. In this paper, an explicit criterion for the selection of the optimal box size in box-assisted algorithms is presented. When used in conjunction with even the simplest box-assisted algorithm, the computation time needed to estimate the correlation integral is drastically reduced. These reductions range from a factor of 10 to factors larger than 1000, depending on the complexity of the attractor and/or the length of the dataset.

Suggested Citation

  • Bueno-Orovio, Alfonso & Pérez-García, Víctor M., 2007. "Enhanced box and prism assisted algorithms for computing the correlation dimension," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 509-518.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:2:p:509-518
    DOI: 10.1016/j.chaos.2006.03.043
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077906002645
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2006.03.043?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. Hsieh, David A, 1991. "Chaos and Nonlinear Dynamics: Application to Financial Markets," Journal of Finance, American Finance Association, vol. 46(5), pages 1839-1877, December.
    2. Pascolo, Paolo & Barazza, Fausto & Carniel, Roberto, 2006. "Considerations on the application of the chaos paradigm to describe the postural sway," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1339-1346.
    3. Silva, F.E. & Gonçalves, L.L. & Fereira, D.B.B. & Rebello, J.M.A., 2005. "Characterization of failure mechanism in composite materials through fractal analysis of acoustic emission signals," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 481-494.
    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. Zhou, Shuang & Wang, Xingyuan & Zhou, Wenjie & Zhang, Chuan, 2022. "Recognition of the scale-free interval for calculating the correlation dimension using machine learning from chaotic time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(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. Kian-Ping Lim & Melvin J. Hinich & Venus Khim-Sen Liew, 2005. "Statistical Inadequacy of GARCH Models for Asian Stock Markets," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 4(3), pages 263-279, December.
    2. Dutta, Shantanu & Essaddam, Naceur & Kumar, Vinod & Saadi, Samir, 2017. "How does electronic trading affect efficiency of stock market and conditional volatility? Evidence from Toronto Stock Exchange," Research in International Business and Finance, Elsevier, vol. 39(PB), pages 867-877.
    3. A. Corcos & J-P Eckmann & A. Malaspinas & Y. Malevergne & D. Sornette, 2002. "Imitation and contrarian behaviour: hyperbolic bubbles, crashes and chaos," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 264-281.
    4. Scott C. Linn & Nicholas S. P. Tay, 2007. "Complexity and the Character of Stock Returns: Empirical Evidence and a Model of Asset Prices Based on Complex Investor Learning," Management Science, INFORMS, vol. 53(7), pages 1165-1180, July.
    5. Ren, Fei & Gu, Gao-Feng & Zhou, Wei-Xing, 2009. "Scaling and memory in the return intervals of realized volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(22), pages 4787-4796.
    6. Javier Morales & V'ictor Tercero & Fernando Camacho & Eduardo Cordero & Luis L'opez & F-Javier Almaguer, 2014. "Trend and Fractality Assessment of Mexico's Stock Exchange," Papers 1411.3399, arXiv.org.
    7. John T. Barkoulas & Christopher F. Baum & Joseph Onochie, 1997. "A nonparametric investigation of the 90‐day t‐bill rate," Review of Financial Economics, John Wiley & Sons, vol. 6(2), pages 187-198.
    8. Takala, Kari & Virén, Matti, 1995. "Testing nonlinear dynamics, long memory and chaotic behaviour with macroeconomic data," Research Discussion Papers 9/1995, Bank of Finland.
    9. Catherine Kyrtsou & Michel Terraza, 2003. "Is it Possible to Study Chaotic and ARCH Behaviour Jointly? Application of a Noisy Mackey–Glass Equation with Heteroskedastic Errors to the Paris Stock Exchange Returns Series," Computational Economics, Springer;Society for Computational Economics, vol. 21(3), pages 257-276, June.
    10. Risso, Wiston Adrián, 2008. "The informational efficiency and the financial crashes," Research in International Business and Finance, Elsevier, vol. 22(3), pages 396-408, September.
    11. repec:zbw:bofrdp:1995_009 is not listed on IDEAS
    12. Urquhart, Andrew & Hudson, Robert, 2013. "Efficient or adaptive markets? Evidence from major stock markets using very long run historic data," International Review of Financial Analysis, Elsevier, vol. 28(C), pages 130-142.
    13. Kian-Ping Lim & Venus Khim-Sen Liew & Hock-Tsen Wong, 2003. "Weak-form Efficient Market Hypothesis, Behavioural Finance and Episodic Transient Dependencies: The Case of the Kuala Lumpur Stock Exchange," Finance 0312012, University Library of Munich, Germany.
    14. Franco Bevilacqua & Adriaan van Zon, 2004. "Random walks and non-linear paths in macroeconomic time series: some evidence and implications," Chapters, in: John Foster & Werner Hölzl (ed.), Applied Evolutionary Economics and Complex Systems, chapter 3, Edward Elgar Publishing.
    15. Semei Coronado-Ram'irez & Pedro Celso-Arellano & Omar Rojas, 2014. "Adaptive Market Efficiency of Agricultural Commodity Futures Contracts," Papers 1412.8017, arXiv.org, revised Mar 2015.
    16. Philip Maymin, 2010. "The Hazards of Propping Up: Bubbles and Chaos," Papers 1002.2282, arXiv.org.
    17. Jialei Jiang & Eun-Mi Park & Seong-Taek Park, 2021. "The Impact of the COVID-19 on Economic Sustainability—A Case Study of Fluctuation in Stock Prices for China and South Korea," Sustainability, MDPI, vol. 13(12), pages 1-17, June.
    18. Gianni Degasperi & Luca Erzegovesi, 1999. "I mercati finanziari come sistemi complessi: il modello di Vaga," Alea Tech Reports 007, Department of Computer and Management Sciences, University of Trento, Italy, revised 14 Jun 2008.
    19. Bollerslev, Tim & Kretschmer, Uta & Pigorsch, Christian & Tauchen, George, 2009. "A discrete-time model for daily S & P500 returns and realized variations: Jumps and leverage effects," Journal of Econometrics, Elsevier, vol. 150(2), pages 151-166, June.
    20. Ali Habibnia & Esfandiar Maasoumi, 2021. "Forecasting in Big Data Environments: An Adaptable and Automated Shrinkage Estimation of Neural Networks (AAShNet)," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 363-381, December.
    21. Rama Cont & Jean-Philippe Bouchaud, 1997. "Herd behavior and aggregate fluctuations in financial markets," Science & Finance (CFM) working paper archive 500028, Science & Finance, Capital Fund Management.

    More about this item

    Statistics

    Access and download statistics

    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:34:y:2007:i:2:p:509-518. 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.