IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v109y2016icp159-167.html
   My bibliography  Save this article

On some estimators of the Hurst index of the solution of SDE driven by a fractional Brownian motion

Author

Listed:
  • Kubilius, K.
  • Skorniakov, V.

Abstract

Strongly consistent and asymptotically normal estimators of the Hurst parameter of solutions of stochastic differential equations are proposed. The estimators are based on discrete observations of the underlying processes.

Suggested Citation

  • Kubilius, K. & Skorniakov, V., 2016. "On some estimators of the Hurst index of the solution of SDE driven by a fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 159-167.
    • Handle: RePEc:eee:stapro:v:109:y:2016:i:c:p:159-167
    DOI: 10.1016/j.spl.2015.11.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715215003818
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2015.11.013?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. Todorov, Viktor, 2013. "Power variation from second order differences for pure jump semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2829-2850.
    2. Jean-Christophe Breton & Jean-François Coeurjolly, 2012. "Confidence intervals for the Hurst parameter of a fractional Brownian motion based on finite sample size," Statistical Inference for Stochastic Processes, Springer, vol. 15(1), pages 1-26, April.
    3. Kubilius, K. & Mishura, Y., 2012. "The rate of convergence of Hurst index estimate for the stochastic differential equation," Stochastic Processes and their Applications, Elsevier, vol. 122(11), pages 3718-3739.
    4. Benassi, Albert & Cohen, Serge & Istas, Jacques & Jaffard, Stéphane, 1998. "Identification of filtered white noises," Stochastic Processes and their Applications, Elsevier, vol. 75(1), pages 31-49, June.
    5. Nualart, David & Ouknine, Youssef, 2002. "Regularization of differential equations by fractional noise," Stochastic Processes and their Applications, Elsevier, vol. 102(1), pages 103-116, 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. Fabienne Comte & Nicolas Marie, 2019. "Nonparametric estimation in fractional SDE," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 359-382, October.
    2. Kubilius, K., 2020. "CLT for quadratic variation of Gaussian processes and its application to the estimation of the Orey index," Statistics & Probability Letters, Elsevier, vol. 165(C).
    3. Kęstutis Kubilius & Aidas Medžiūnas, 2020. "Positive Solutions of the Fractional SDEs with Non-Lipschitz Diffusion Coefficient," Mathematics, MDPI, vol. 9(1), pages 1-14, December.

    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. Kęstutis Kubilius & Dmitrij Melichov, 2016. "Exact Confidence Intervals of the Extended Orey Index for Gaussian Processes," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 785-804, September.
    2. Kubilius, K. & Mishura, Y., 2012. "The rate of convergence of Hurst index estimate for the stochastic differential equation," Stochastic Processes and their Applications, Elsevier, vol. 122(11), pages 3718-3739.
    3. 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.
    4. Hounyo, Ulrich & Varneskov, Rasmus T., 2017. "A local stable bootstrap for power variations of pure-jump semimartingales and activity index estimation," Journal of Econometrics, Elsevier, vol. 198(1), pages 10-28.
    5. Coffie, Emmanuel & Duedahl, Sindre & Proske, Frank, 2023. "Sensitivity analysis with respect to a stochastic stock price model with rough volatility via a Bismut–Elworthy–Li formula for singular SDEs," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 156-195.
    6. Marc Mukendi Mpanda & Safari Mukeru & Mmboniseni Mulaudzi, 2020. "Generalisation of Fractional-Cox-Ingersoll-Ross Process," Papers 2008.07798, arXiv.org, revised Jul 2022.
    7. Peng, Qidi, 2011. "Uniform Hölder exponent of a stationary increments Gaussian process: Estimation starting from average values," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1326-1335, August.
    8. Lee Jeonghwa, 2021. "Generalized Bernoulli process: simulation, estimation, and application," Dependence Modeling, De Gruyter, vol. 9(1), pages 141-155, January.
    9. Alexandre Brouste & Hiroki Masuda, 2018. "Efficient estimation of stable Lévy process with symmetric jumps," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 289-307, July.
    10. Pilipenko, Andrey & Proske, Frank Norbert, 2018. "On perturbations of an ODE with non-Lipschitz coefficients by a small self-similar noise," Statistics & Probability Letters, Elsevier, vol. 132(C), pages 62-73.
    11. Z. Merrick Li & Oliver Linton, 2022. "A ReMeDI for Microstructure Noise," Econometrica, Econometric Society, vol. 90(1), pages 367-389, January.
    12. Xiliang Fan, 2019. "Derivative Formulas and Applications for Degenerate Stochastic Differential Equations with Fractional Noises," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1360-1381, September.
    13. Todorov, Viktor, 2019. "Nonparametric inference for the spectral measure of a bivariate pure-jump semimartingale," Stochastic Processes and their Applications, Elsevier, vol. 129(2), pages 419-451.
    14. Jan Gairing & Peter Imkeller & Radomyra Shevchenko & Ciprian Tudor, 2020. "Hurst Index Estimation in Stochastic Differential Equations Driven by Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1691-1714, September.
    15. David Baños & Salvador Ortiz-Latorre & Andrey Pilipenko & Frank Proske, 2022. "Strong Solutions of Stochastic Differential Equations with Generalized Drift and Multidimensional Fractional Brownian Initial Noise," Journal of Theoretical Probability, Springer, vol. 35(2), pages 714-771, June.
    16. Kohei Chiba, 2019. "Estimation of the lead–lag parameter between two stochastic processes driven by fractional Brownian motions," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 323-357, October.
    17. Kubilius, K. & Skorniakov, V., 2017. "A short note on a class of statistics for estimation of the Hurst index of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 78-82.
    18. Mishura, Yu. & Nualart, D., 2004. "Weak solutions for stochastic differential equations with additive fractional noise," Statistics & Probability Letters, Elsevier, vol. 70(4), pages 253-261, December.
    19. Nourdin, Ivan & Peccati, Giovanni & Viens, Frederi G., 2014. "Comparison inequalities on Wiener space," Stochastic Processes and their Applications, Elsevier, vol. 124(4), pages 1566-1581.
    20. Es-Sebaiy, Khalifa & Ouassou, Idir & Ouknine, Youssef, 2009. "Estimation of the drift of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1647-1653, July.

    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:stapro:v:109:y:2016:i:c:p:159-167. 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/622892/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.