IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v389y2010i1p100-106.html
   My bibliography  Save this article

A long-range memory stochastic model of the return in financial markets

Author

Listed:
  • Gontis, V.
  • Ruseckas, J.
  • Kononovičius, A.

Abstract

We present a nonlinear stochastic differential equation (SDE) which mimics the probability density function (PDF) of the return and the power spectrum of the absolute return in financial markets. Absolute return as a measure of market volatility is considered in the proposed model as a long-range memory stochastic variable. The SDE is obtained from the analogy with an earlier proposed model of trading activity in the financial markets and generalized within the nonextensive statistical mechanics framework. The proposed stochastic model generates time series of the return with two power law statistics, i.e., the PDF and the power spectral density, reproducing the empirical data for the one-minute trading return in the NYSE.

Suggested Citation

  • Gontis, V. & Ruseckas, J. & Kononovičius, A., 2010. "A long-range memory stochastic model of the return in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(1), pages 100-106.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:1:p:100-106
    DOI: 10.1016/j.physa.2009.09.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843710900747X
    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.2009.09.011?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. Silvio M. Duarte Queiros & Celia Anteneodo & Constantino Tsallis, 2005. "Power-law distributions in economics: a nonextensive statistical approach," Papers physics/0503024, arXiv.org.
    2. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
    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. Kononovicius, A. & Ruseckas, J., 2015. "Nonlinear GARCH model and 1/f noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 74-81.
    2. Vygintas Gontis & Aleksejus Kononovicius, 2014. "Consentaneous Agent-Based and Stochastic Model of the Financial Markets," PLOS ONE, Public Library of Science, vol. 9(7), pages 1-12, July.
    3. Xiao, Weilin & Zhang, Weiguo & Zhang, Xili & Chen, Xiaoyan, 2014. "The valuation of equity warrants under the fractional Vasicek process of the short-term interest rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 320-337.
    4. Ponta, Linda & Trinh, Mailan & Raberto, Marco & Scalas, Enrico & Cincotti, Silvano, 2019. "Modeling non-stationarities in high-frequency financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 173-196.
    5. Kononovicius, Aleksejus & Kazakevičius, Rytis & Kaulakys, Bronislovas, 2022. "Resemblance of the power-law scaling behavior of a non-Markovian and nonlinear point processes," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    6. Aleksejus Kononovicius & Rytis Kazakeviv{c}ius & Bronislovas Kaulakys, 2022. "Resemblance of the power-law scaling behavior of a non-Markovian and nonlinear point processes," Papers 2205.07563, arXiv.org, revised Jul 2022.
    7. Vygintas Gontis & Aleksejus Kononovicius, 2017. "Spurious memory in non-equilibrium stochastic models of imitative behavior," Papers 1707.09801, arXiv.org.
    8. Aleksejus Kononovicius & Julius Ruseckas, 2014. "Nonlinear GARCH model and 1/f noise," Papers 1412.6244, arXiv.org, revised Feb 2015.
    9. Rytis Kazakevicius & Aleksejus Kononovicius & Bronislovas Kaulakys & Vygintas Gontis, 2021. "Understanding the nature of the long-range memory phenomenon in socioeconomic systems," Papers 2108.02506, arXiv.org, revised Aug 2021.
    10. Aleksejus Kononovicius & Valentas Daniunas, 2013. "Agent-based and macroscopic modeling of the complex socio-economic systems," Papers 1303.3693, arXiv.org, revised Apr 2013.

    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. Sabrina Camargo & Silvio M. Duarte Queiros & Celia Anteneodo, 2013. "Bridging stylized facts in finance and data non-stationarities," Papers 1302.3197, arXiv.org, revised May 2013.
    2. Barunik, Jozef & Vacha, Lukas, 2010. "Monte Carlo-based tail exponent estimator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4863-4874.
    3. Dash, Saumya Ranjan & Maitra, Debasish, 2018. "Does sentiment matter for stock returns? Evidence from Indian stock market using wavelet approach," Finance Research Letters, Elsevier, vol. 26(C), pages 32-39.
    4. Lallouache, Mehdi & Abergel, Frédéric, 2014. "Tick size reduction and price clustering in a FX order book," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 488-498.
    5. Aviral Tiwari & Niyati Bhanja & Arif Dar & Faridul Islam, 2015. "Time–frequency relationship between share prices and exchange rates in India: Evidence from continuous wavelets," Empirical Economics, Springer, vol. 48(2), pages 699-714, March.
    6. Dufour, Jean-Marie & García, René & Taamouti, Abderrahim, 2008. "Measuring causality between volatility and returns with high-frequency data," UC3M Working papers. Economics we084422, Universidad Carlos III de Madrid. Departamento de Economía.
    7. Bence Toth & Janos Kertesz, 2009. "The Epps effect revisited," Quantitative Finance, Taylor & Francis Journals, vol. 9(7), pages 793-802.
    8. Do, Hung Xuan & Brooks, Robert & Treepongkaruna, Sirimon & Wu, Eliza, 2014. "How does trading volume affect financial return distributions?," International Review of Financial Analysis, Elsevier, vol. 35(C), pages 190-206.
    9. W.-S. Jung & F. Z. Wang & S. Havlin & T. Kaizoji & H.-T. Moon & H. E. Stanley, 2008. "Volatility return intervals analysis of the Japanese market," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 62(1), pages 113-119, March.
    10. Kaijian He & Rui Zha & Jun Wu & Kin Keung Lai, 2016. "Multivariate EMD-Based Modeling and Forecasting of Crude Oil Price," Sustainability, MDPI, vol. 8(4), pages 1-11, April.
    11. Ozcan Ceylan, 2015. "Limited information-processing capacity and asymmetric stock correlations," Quantitative Finance, Taylor & Francis Journals, vol. 15(6), pages 1031-1039, June.
    12. Beine, Michel & Laurent, Sébastien & Palm, Franz C., 2009. "Central bank FOREX interventions assessed using realized moments," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 19(1), pages 112-127, February.
    13. Scalas, Enrico & Kaizoji, Taisei & Kirchler, Michael & Huber, Jürgen & Tedeschi, Alessandra, 2006. "Waiting times between orders and trades in double-auction markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 463-471.
    14. Nour Meddahi, 2002. "A theoretical comparison between integrated and realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 479-508.
    15. Andrea Terzi, 2003. "Is a transactions tax an effective means to stabilize the foreign exchange market?," BNL Quarterly Review, Banca Nazionale del Lavoro, vol. 56(227), pages 367-385.
    16. Malgorzata Doman, 2008. "Information Impact on Stock Price Dynamics," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 8, pages 13-20.
    17. Torben G. ANDERSEN & Tim BOLLERSLEV & Nour MEDDAHI, 2002. "Correcting The Errors : A Note On Volatility Forecast Evaluation Based On High-Frequency Data And Realized Volatilities," Cahiers de recherche 21-2002, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    18. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 1-30.
    19. Monira Essa Aloud, 2016. "Time Series Analysis Indicators under Directional Changes: The Case of Saudi Stock Market," International Journal of Economics and Financial Issues, Econjournals, vol. 6(1), pages 55-64.
    20. Roxana Chiriac & Valeri Voev, 2011. "Modelling and forecasting multivariate realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(6), pages 922-947, September.

    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:389:y:2010:i:1:p:100-106. 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.