IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v117y2007i4p476-486.html
   My bibliography  Save this article

Quadratic variations of spherical fractional Brownian motions

Author

Listed:
  • Istas, Jacques

Abstract

We prove the convergence and the asymptotic normality of the quadratic variations of the spherical fractional Brownian motion.

Suggested Citation

  • Istas, Jacques, 2007. "Quadratic variations of spherical fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 117(4), pages 476-486, April.
  • Handle: RePEc:eee:spapps:v:117:y:2007:i:4:p:476-486
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(06)00121-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Benassi, Albert & Cohen, Serge & Istas, Jacques, 1998. "Identifying the multifractional function of a Gaussian process," Statistics & Probability Letters, Elsevier, vol. 39(4), pages 337-345, August.
    2. Adler, Robert J. & Pyke, Ron, 1993. "Uniform quadratic variation for Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 48(2), pages 191-209, November.
    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. Lan, Xiaohong & Xiao, Yimin, 2018. "Strong local nondeterminism of spherical fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 44-50.

    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. Ayoub Ammy-Driss & Matthieu Garcin, 2021. "Efficiency of the financial markets during the COVID-19 crisis: time-varying parameters of fractional stable dynamics," Working Papers hal-02903655, HAL.
    2. Ayache, Antoine & Lévy Véhel, Jacques, 2004. "On the identification of the pointwise Hölder exponent of the generalized multifractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 119-156, May.
    3. Pierre R. Bertrand & Marie-Eliette Dury & Bing Xiao, 2020. "A study of Chinese market efficiency, Shanghai versus Shenzhen: Evidence based on multifractional models," Post-Print hal-03031766, HAL.
    4. Garcin, Matthieu, 2017. "Estimation of time-dependent Hurst exponents with variational smoothing and application to forecasting foreign exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 462-479.
    5. Bardet, Jean-Marc & Surgailis, Donatas, 2013. "Nonparametric estimation of the local Hurst function of multifractional Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 1004-1045.
    6. repec:jss:jstsof:23:i01 is not listed on IDEAS
    7. Bégyn, Arnaud, 2007. "Functional limit theorems for generalized quadratic variations of Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1848-1869, December.
    8. Frezza, Massimiliano & Bianchi, Sergio & Pianese, Augusto, 2021. "Fractal analysis of market (in)efficiency during the COVID-19," Finance Research Letters, Elsevier, vol. 38(C).
    9. Pierre R. Bertrand & Abdelkader Hamdouni & Samia Khadhraoui, 2012. "Modelling NASDAQ Series by Sparse Multifractional Brownian Motion," Methodology and Computing in Applied Probability, Springer, vol. 14(1), pages 107-124, March.
    10. Stoev, Stilian & Taqqu, Murad S. & Park, Cheolwoo & Michailidis, George & Marron, J.S., 2006. "LASS: a tool for the local analysis of self-similarity," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2447-2471, May.
    11. Ammy-Driss, Ayoub & Garcin, Matthieu, 2023. "Efficiency of the financial markets during the COVID-19 crisis: Time-varying parameters of fractional stable dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    12. Matthieu Garcin & Martino Grasselli, 2022. "Long versus short time scales: the rough dilemma and beyond," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 257-278, June.
    13. Mohamed Boutahar & Gilles Dufrénot & Anne Péguin-Feissolle, 2008. "A Simple Fractionally Integrated Model with a Time-varying Long Memory Parameter d t," Computational Economics, Springer;Society for Computational Economics, vol. 31(3), pages 225-241, April.
    14. Massimiliano Frezza & Sergio Bianchi & Augusto Pianese, 2022. "Forecasting Value-at-Risk in turbulent stock markets via the local regularity of the price process," Computational Management Science, Springer, vol. 19(1), pages 99-132, January.
    15. Ayoub Ammy-Driss & Matthieu Garcin, 2020. "Efficiency of the financial markets during the COVID-19 crisis: time-varying parameters of fractional stable dynamics," Papers 2007.10727, arXiv.org, revised Nov 2021.
    16. Marco Dozzi & Yuliya Mishura & Georgiy Shevchenko, 2015. "Asymptotic behavior of mixed power variations and statistical estimation in mixed models," Statistical Inference for Stochastic Processes, Springer, vol. 18(2), pages 151-175, July.
    17. Tsionas, Mike G., 2021. "Bayesian analysis of static and dynamic Hurst parameters under stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    18. Perrin, Olivier, 1999. "Quadratic variation for Gaussian processes and application to time deformation," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 293-305, August.
    19. Fabrice Gamboa & Jean-Michel Loubes, 2007. "Estimation of parameters of a multifractal process," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 383-407, August.
    20. Matthieu Garcin, 2019. "Fractal analysis of the multifractality of foreign exchange rates [Analyse fractale de la multifractalité des taux de change]," Working Papers hal-02283915, HAL.
    21. Vu, Huong T.L. & Richard, Frédéric J.P., 2020. "Statistical tests of heterogeneity for anisotropic multifractional Brownian fields," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4667-4692.

    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:spapps:v:117:y:2007:i:4:p:476-486. 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.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.