IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v344y2004i1p244-251.html
   My bibliography  Save this article

Remarks on the possible universal mechanism of the non-linear long-term autocorrelations in financial time-series

Author

Listed:
  • Kutner, Ryszard
  • Świtała, Filip

Abstract

The paper consists of two parts: (i) the empirical one where the non-linear, long-term autocorrelations present in high-frequency data extracting from the Warsaw Stock Exchange were analyzed and (ii) theoretical one where predictions of our model (Quantitative Finance 3 (2003) 201; Physica A (2003); Chem. Phys. 284 (2002) 481; Phys. Comm. 147 (2002) 565; Physica A 264 (1999) 84; Physica A 264 (1999) 107; Lecture Notes in Computer Science 2657 (2003) 407; Eur. Phys. J. B 33 (2003) 495) were shown and discussed. This model introduces the possibility that the Weierstrass (hierarchical) random walk can be occasionally intermitted by momentary localizations; the localizations themselves are again described by the Weierstrass process. In other words, this combined walk is a kind of the non-separable, generalized continuous-time random walk formalism. To adapt the model to the description of empirical data recorded at time horizon Δt=1min, we applied a discretization procedure into the continuous-time series produced by the model. We observed that such a procedure generates the non-linear, long-term autocorrelations even in the Gaussian regime, as turning points of the random walk trajectory are, most often, incommensurable with discretization time-step. These autocorrelations appear to be similar to those observed in the financial time series (Physica A 287 (2000) 396; Physica A 299 (2001) 1; Physica A 299 (2001) 16; Physica A 299 (2001) 28), although single steps of the walker within continuous time are, by definition, uncorrelated. Our approach suggests a surprising origin of the non-linear, long-term autocorrelations alternative to the one proposed very recently (cf. Phys. Rev. E 67 (2003) 021112 and refs. therein) although both approaches involve related variants of the well-known CTRW formalism applied in yet many different branches of knowledge (Phys. Rep. 158 (1987) 263; Phys. Rep. 195 (1990) 127; in: A. Bunde, S. Havlin (Eds.), Fractals in Science, Springer, Berlin, 1995, pp. 119–161).

Suggested Citation

  • Kutner, Ryszard & Świtała, Filip, 2004. "Remarks on the possible universal mechanism of the non-linear long-term autocorrelations in financial time-series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 244-251.
    • Handle: RePEc:eee:phsmap:v:344:y:2004:i:1:p:244-251
    DOI: 10.1016/j.physa.2004.06.126
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437104009434
    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.2004.06.126?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. Metzler, Ralf & Klafter, Joseph, 2000. "Boundary value problems for fractional diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(1), pages 107-125.
    2. Kehr, K.W. & Kutner, R., 1982. "Random walk on a random walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 110(3), pages 535-549.
    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. Marcin Wk{a}torek & Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marek Stanuszek, 2020. "Multiscale characteristics of the emerging global cryptocurrency market," Papers 2010.15403, arXiv.org, revised Mar 2021.

    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. Marseguerra, Marzio & Zoia, Andrea, 2008. "Pre-asymptotic corrections to fractional diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 2668-2674.
    2. Khan, Sharon & Reynolds, Andy M., 2005. "Derivation of a Fokker–Planck equation for generalized Langevin dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 183-188.
    3. Balakrishnan, V. & Van den Broeck, C., 1995. "Transport properties on a random comb," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 217(1), pages 1-21.
    4. D’Ovidio, Mirko, 2012. "From Sturm–Liouville problems to fractional and anomalous diffusions," Stochastic Processes and their Applications, Elsevier, vol. 122(10), pages 3513-3544.
    5. Wei, T. & Li, Y.S., 2018. "Identifying a diffusion coefficient in a time-fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 151(C), pages 77-95.
    6. Hosseininia, M. & Heydari, M.H., 2019. "Meshfree moving least squares method for nonlinear variable-order time fractional 2D telegraph equation involving Mittag–Leffler non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 389-399.
    7. Spišák, Daniel, 1994. "Two-dimensional diffusion of particles with dipolar-like interaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 209(1), pages 42-50.
    8. Wang, Shaowei & Zhao, Moli & Li, Xicheng, 2011. "Radial anomalous diffusion in an annulus," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3397-3403.
    9. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    10. Muszkieta, Monika & Janczura, Joanna & Weron, Aleksander, 2021. "Simulation and tracking of fractional particles motion. From microscopy video to statistical analysis. A Brownian bridge approach," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    11. Xian, Jun & Yan, Xiong-bin & Wei, Ting, 2020. "Simultaneous identification of three parameters in a time-fractional diffusion-wave equation by a part of boundary Cauchy data," Applied Mathematics and Computation, Elsevier, vol. 384(C).
    12. Mophou, G. & Tao, S. & Joseph, C., 2015. "Initial value/boundary value problem for composite fractional relaxation equation," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 134-144.
    13. Guo, Gang & Li, Kun & Wang, Yuhui, 2015. "Exact solutions of a modified fractional diffusion equation in the finite and semi-infinite domains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 193-201.
    14. Marseguerra, M. & Zoia, A., 2008. "Monte Carlo evaluation of FADE approach to anomalous kinetics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(4), pages 345-357.
    15. Al-Mdallal, Qasem M., 2009. "An efficient method for solving fractional Sturm–Liouville problems," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 183-189.
    16. Kashfi Sadabad, Mahnaz & Jodayree Akbarfam, Aliasghar, 2021. "An efficient numerical method for estimating eigenvalues and eigenfunctions of fractional Sturm–Liouville problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 547-569.
    17. Wei, Q. & Yang, S. & Zhou, H.W. & Zhang, S.Q. & Li, X.N. & Hou, W., 2021. "Fractional diffusion models for radionuclide anomalous transport in geological repository systems," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    18. Huckaby, Dale A. & Hubbard, Joseph B., 1983. "A random walk on a random channel with absorbing barriers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 122(3), pages 602-610.
    19. Alam, Mehboob & Shah, Dildar, 2021. "Hyers–Ulam stability of coupled implicit fractional integro-differential equations with Riemann–Liouville derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    20. Guo, Gang & Chen, Bin & Zhao, Xinjun & Zhao, Fang & Wang, Quanmin, 2015. "First passage time distribution of a modified fractional diffusion equation in the semi-infinite interval," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 279-290.

    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:344:y:2004:i:1:p:244-251. 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.