IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2507.15437.html
   My bibliography  Save this paper

Prediction of linear fractional stable motions using codifference, with application to non-Gaussian rough volatility

Author

Listed:
  • Matthieu Garcin
  • Karl Sawaya
  • Thomas Valade

Abstract

The linear fractional stable motion (LFSM) extends the fractional Brownian motion (fBm) by considering $\alpha$-stable increments. We propose a method to forecast future increments of the LFSM from past discrete-time observations, using the conditional expectation when $\alpha>1$ or a semimetric projection otherwise. It relies on the codifference, which describes the serial dependence of the process, instead of the covariance. Indeed, covariance is commonly used for predicting an fBm but it is infinite when $\alpha

Suggested Citation

  • Matthieu Garcin & Karl Sawaya & Thomas Valade, 2025. "Prediction of linear fractional stable motions using codifference, with application to non-Gaussian rough volatility," Papers 2507.15437, arXiv.org, revised Nov 2025.
    • Handle: RePEc:arx:papers:2507.15437
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2507.15437
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. S. Bianchi & A. Pantanella & A. Pianese, 2013. "Modeling stock prices by multifractional Brownian motion: an improved estimation of the pointwise regularity," Quantitative Finance, Taylor & Francis Journals, vol. 13(8), pages 1317-1330, July.
    2. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous‐time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323, October.
    3. Phillipe Lambert & J. K. Lindsey, 1999. "Analysing Financial Returns by Using Regression Models Based on Non‐Symmetric Stable Distributions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(3), pages 409-424.
    4. Piotr S. Kokoszka & Murad S. Taqqu, 1994. "Infinite Variance Stable Arma Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(2), pages 203-220, March.
    5. Dedi Rosadi & Manfred Deistler, 2011. "Estimating the codifference function of linear time series models with infinite variance," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(3), pages 395-429, May.
    6. Rafal Weron, 1996. "Correction to: "On the Chambers-Mallows-Stuck Method for Simulating Skewed Stable Random Variables"," HSC Research Reports HSC/96/01, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    7. Mathias Mørck Ljungdahl & Mark Podolskij, 2020. "A minimal contrast estimator for the linear fractional stable motion," Statistical Inference for Stochastic Processes, Springer, vol. 23(2), pages 381-413, July.
    8. Markus Bibinger & Jun Yu & Chen Zhang, 2025. "Modeling and Forecasting Realized Volatility with Multivariate Fractional Brownian Motion," Papers 2504.15985, arXiv.org.
    9. 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.
    10. Hu, Yaozhong & Nualart, David, 2010. "Parameter estimation for fractional Ornstein-Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 1030-1038, June.
    11. Weron, Rafal, 1996. "On the Chambers-Mallows-Stuck method for simulating skewed stable random variables," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 165-171, June.
    12. Ayache, Antoine & Hamonier, Julien, 2012. "Linear fractional stable motion: A wavelet estimator of the α parameter," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1569-1575.
    13. Surgailis, Donatas & Teyssière, Gilles & Vaiciulis, Marijus, 2008. "The increment ratio statistic," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 510-541, March.
    14. Rama Cont & Purba Das, 2024. "Rough Volatility: Fact or Artefact?," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(1), pages 191-223, May.
    15. Miller, Grady, 1978. "Properties of certain symmetric stable distributions," Journal of Multivariate Analysis, Elsevier, vol. 8(3), pages 346-360, September.
    16. Coeurjolly, Jean-Francois, 2000. "Simulation and identification of the fractional Brownian motion: a bibliographical and comparative study," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 5(i07).
    17. Brouty, Xavier & Garcin, Matthieu, 2024. "Fractal properties, information theory, and market efficiency," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    18. Eduardo Abi Jaber & Nathan De Carvalho, 2023. "Reconciling rough volatility with jumps," Papers 2303.07222, arXiv.org, revised Sep 2024.
    19. Pipiras, Vladas & Taqqu, Murad S. & Abry, Patrice, 2003. "Can continuous-time stationary stable processes have discrete linear representations?," Statistics & Probability Letters, Elsevier, vol. 64(2), pages 147-157, August.
    20. Viitasaari, Lauri, 2016. "Representation of stationary and stationary increment processes via Langevin equation and self-similar processes," Statistics & Probability Letters, Elsevier, vol. 115(C), pages 45-53.
    21. Eduardo Abi Jaber & Shaun (Xiaoyuan) Li, 2025. "Volatility Models in Practice: Rough, Path‐Dependent, or Markovian?," Mathematical Finance, Wiley Blackwell, vol. 35(4), pages 796-817, October.
    22. Eduardo Abi Jaber & Nathan de Carvalho, 2024. "Reconciling rough volatility with jumps," Post-Print hal-04295416, HAL.
    23. Matthieu Garcin, 2022. "Forecasting with fractional Brownian motion: a financial perspective," Quantitative Finance, Taylor & Francis Journals, vol. 22(8), pages 1495-1512, August.
    24. Eduardo Abi Jaber & Shaun & Li, 2024. "Volatility models in practice: Rough, Path-dependent or Markovian?," Papers 2401.03345, arXiv.org, revised Apr 2025.
    25. Alfeus, Mesias & Mwampashi, Muthe M. & Nikitopoulos, Christina S. & Overbeck, Ludger, 2025. "Stochastic modelling and forecasting of wind capacity utilization with applications to risk management: The Australian case," Pacific-Basin Finance Journal, Elsevier, vol. 91(C).
    Full references (including those not matched with items on IDEAS)

    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. Daniele Angelini & Matthieu Garcin, 2024. "Market information of the fractional stochastic regularity model," Papers 2409.07159, arXiv.org, revised May 2025.
    2. Angelini, Daniele & Bianchi, Sergio, 2023. "Nonlinear biases in the roughness of a Fractional Stochastic Regularity Model," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    3. Takaishi, Tetsuya, 2025. "Multifractality and sample size influence on Bitcoin volatility patterns," Finance Research Letters, Elsevier, vol. 74(C).
    4. Sergio Bianchi & Daniele Angelini & Massimiliano Frezza & Augusto Pianese, 2025. "From fair price to fair volatility: Towards an Efficiency-Consistent Definition of Financial Risk," Papers 2508.11649, arXiv.org.
    5. Rami Ahmad El-Nabulsi & Waranont Anukool, 2025. "Qualitative financial modelling in fractal dimensions," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 11(1), pages 1-47, December.
    6. Li, Yicun & Teng, Yuanyang, 2023. "Statistical inference in discretely observed fractional Ornstein–Uhlenbeck processes," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    7. Sergio Bianchi & Daniele Angelini, 2025. "Fair Volatility: A Framework for Reconceptualizing Financial Risk," Papers 2509.18837, arXiv.org.
    8. Eduardo Abi Jaber & Shaun Xiaoyuan Li, 2025. "Volatility models in practice: Rough, Path-dependent or Markovian?," Post-Print hal-04372797, HAL.
    9. Furrer, Hansjorg & Michna, Zbigniew & Weron, Aleksander, 1997. "Stable Lévy motion approximation in collective risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 20(2), pages 97-114, September.
    10. Dassios, Angelos & Qu, Yan & Zhao, Hongbiao, 2018. "Exact simulation for a class of tempered stable," LSE Research Online Documents on Economics 86981, London School of Economics and Political Science, LSE Library.
    11. Xu, Weijun & Sun, Qi & Xiao, Weilin, 2012. "A new energy model to capture the behavior of energy price processes," Economic Modelling, Elsevier, vol. 29(5), pages 1585-1591.
    12. J.-F. Chamayou, 2001. "Pseudo random numbers for the Landau and Vavilov distributions," Computational Statistics, Springer, vol. 16(1), pages 131-152, March.
    13. Weron, Rafał, 2004. "Computationally intensive Value at Risk calculations," Papers 2004,32, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    14. Ranieri Dugo & Giacomo Giorgio & Paolo Pigato, 2024. "The Multivariate Fractional Ornstein-Uhlenbeck Process," CEIS Research Paper 581, Tor Vergata University, CEIS, revised 28 Aug 2024.
    15. Luc Devroye & Lancelot James, 2014. "On simulation and properties of the stable law," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(3), pages 307-343, August.
    16. Khalifa Es-Sebaiy & Mohammed Es.Sebaiy, 2021. "Estimating drift parameters in a non-ergodic Gaussian Vasicek-type model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(2), pages 409-436, June.
    17. Eduardo Abi Jaber & Elie Attal, 2025. "Simulating integrated Volterra square-root processes and Volterra Heston models via Inverse Gaussian," Papers 2504.19885, arXiv.org.
    18. Tsionas, Mike, 2012. "Simple techniques for likelihood analysis of univariate and multivariate stable distributions: with extensions to multivariate stochastic volatility and dynamic factor models," MPRA Paper 40966, University Library of Munich, Germany, revised 20 Aug 2012.
    19. Bondarenko, Valeria & Bondarenko, Victor & Truskovskyi, Kyryl, 2017. "Forecasting of time data with using fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 97(C), pages 44-50.
    20. John C. Frain, 2007. "Small sample power of tests of normality when the alternative is an alpha-stable distribution," Trinity Economics Papers tep0207, Trinity College Dublin, Department of Economics.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:2507.15437. 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.