IDEAS home Printed from https://ideas.repec.org/p/arx/papers/0910.1394.html
   My bibliography  Save this paper

Statistical mixing and aggregation in Feller diffusion

Author

Listed:
  • Celia Anteneodo
  • Silvio M. Duarte Queiros

Abstract

We consider Feller mean-reverting square-root diffusion, which has been applied to model a wide variety of processes with linearly state-dependent diffusion, such as stochastic volatility and interest rates in finance, and neuronal and populations dynamics in natural sciences. We focus on the statistical mixing (or superstatistical) process in which the parameter related to the mean value can fluctuate - a plausible mechanism for the emergence of heavy-tailed distributions. We obtain analytical results for the associated probability density function (both stationary and time dependent), its correlation structure and aggregation properties. Our results are applied to explain the statistics of stock traded volume at different aggregation scales.

Suggested Citation

  • Celia Anteneodo & Silvio M. Duarte Queiros, 2009. "Statistical mixing and aggregation in Feller diffusion," Papers 0910.1394, arXiv.org.
    • Handle: RePEc:arx:papers:0910.1394
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/0910.1394
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Sarah-Kathryn McDonald, 1987. "Book review," Policy Sciences, Springer;Society of Policy Sciences, vol. 20(1), pages 77-79, April.
    2. T. Kaizoji & D. Sornette, 2008. "Market bubbles and crashes," Papers 0812.2449, arXiv.org.
    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. dos Santos, M.A.F. & Colombo, E.H. & Anteneodo, C., 2021. "Random diffusivity scenarios behind anomalous non-Gaussian diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 152(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. Li Lin & Didier Sornette, 2009. "Diagnostics of Rational Expectation Financial Bubbles with Stochastic Mean-Reverting Termination Times," Papers 0911.1921, arXiv.org.
    2. V. Filimonov & G. Demos & D. Sornette, 2017. "Modified profile likelihood inference and interval forecast of the burst of financial bubbles," Quantitative Finance, Taylor & Francis Journals, vol. 17(8), pages 1167-1186, August.
    3. Jiang, Zhi-Qiang & Zhou, Wei-Xing & Sornette, Didier & Woodard, Ryan & Bastiaensen, Ken & Cauwels, Peter, 2010. "Bubble diagnosis and prediction of the 2005-2007 and 2008-2009 Chinese stock market bubbles," Journal of Economic Behavior & Organization, Elsevier, vol. 74(3), pages 149-162, June.
    4. Riza Demirer & Guilherme Demos & Rangan Gupta & Didier Sornette, 2019. "On the predictability of stock market bubbles: evidence from LPPLS confidence multi-scale indicators," Quantitative Finance, Taylor & Francis Journals, vol. 19(5), pages 843-858, May.
    5. Damian Smug & Peter Ashwin & Didier Sornette, 2018. "Predicting financial market crashes using ghost singularities," PLOS ONE, Public Library of Science, vol. 13(3), pages 1-20, March.
    6. Didier Sornette & Ryan Woodard, 2009. "Financial Bubbles, Real Estate bubbles, Derivative Bubbles, and the Financial and Economic Crisis," Papers 0905.0220, arXiv.org.
    7. D. Sornette & R. Woodard, "undated". "Financial Bubbles, Real Estate bubbles, Derivative Bubbles, and the Financial and Economic Crisis," Working Papers CCSS-09-003, ETH Zurich, Chair of Systems Design.
    8. Markus Vogl, 2022. "Quantitative modelling frontiers: a literature review on the evolution in financial and risk modelling after the financial crisis (2008–2019)," SN Business & Economics, Springer, vol. 2(12), pages 1-69, December.
    9. Helmut Herwartz & Konstantin A. Kholodilin, 2014. "In‐Sample and Out‐of‐Sample Prediction of stock Market Bubbles: Cross‐Sectional Evidence," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(1), pages 15-31, January.
    10. Leiss, Matthias & Nax, Heinrich H. & Sornette, Didier, 2015. "Super-exponential growth expectations and the global financial crisis," LSE Research Online Documents on Economics 65434, London School of Economics and Political Science, LSE Library.

    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:arx:papers:0910.1394. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.