IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v173y2024ics0304414924000784.html
   My bibliography  Save this article

Non-asymptotic statistical tests of the diffusion coefficient of stochastic differential equations

Author

Listed:
  • Melnykova, Anna
  • Reynaud-Bouret, Patricia
  • Samson, Adeline

Abstract

We develop several statistical tests of the determinant of the diffusion coefficient of a stochastic differential equation, based on discrete observations on a time interval [0,T] sampled with a time step Δ. Our main contribution is to control the test Type I and Type II errors in a non asymptotic setting, i.e. when the number of observations and the time step are fixed. The test statistics are calculated from the process increments. In dimension 1, the density of the test statistic is explicit. In dimension 2, the test statistic has no explicit density but upper and lower bounds are proved. We also propose a multiple testing procedure in dimension greater than 2. Every test is proved to be of a given non-asymptotic level and separability conditions to control their power are also provided. A numerical study illustrates the properties of the tests for stochastic processes with known or estimated drifts.

Suggested Citation

  • Melnykova, Anna & Reynaud-Bouret, Patricia & Samson, Adeline, 2024. "Non-asymptotic statistical tests of the diffusion coefficient of stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    • Handle: RePEc:eee:spapps:v:173:y:2024:i:c:s0304414924000784
    DOI: 10.1016/j.spa.2024.104372
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414924000784
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2024.104372?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. Mark Podolskij & Mathieu Rosenbaum, 2012. "Testing the local volatility assumption: a statistical approach," Annals of Finance, Springer, vol. 8(1), pages 31-48, February.
    2. Joshua H Goldwyn & Eric Shea-Brown, 2011. "The What and Where of Adding Channel Noise to the Hodgkin-Huxley Equations," PLOS Computational Biology, Public Library of Science, vol. 7(11), pages 1-9, November.
    3. Dette, Holger & Podolskij, Mark, 2008. "Testing the parametric form of the volatility in continuous time diffusion models--a stochastic process approach," Journal of Econometrics, Elsevier, vol. 143(1), pages 56-73, March.
    4. Ditlevsen, Susanne & Löcherbach, Eva, 2017. "Multi-class oscillating systems of interacting neurons," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 1840-1869.
    5. Robert, Christian, 1990. "On some accurate bounds for the quantiles of a non-central chi squared distribution," Statistics & Probability Letters, Elsevier, vol. 10(2), pages 101-106, July.
    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. Susanne Ditlevsen & Adeline Samson, 2019. "Hypoelliptic diffusions: filtering and inference from complete and partial observations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(2), pages 361-384, April.
    2. Quentin Clairon & Adeline Samson, 2022. "Optimal control for parameter estimation in partially observed hypoelliptic stochastic differential equations," Computational Statistics, Springer, vol. 37(5), pages 2471-2491, November.
    3. Kim Christensen & Ulrich Hounyo & Mark Podolskij, 2017. "Is the diurnal pattern sufficient to explain the intraday variation in volatility? A nonparametric assessment," CREATES Research Papers 2017-30, Department of Economics and Business Economics, Aarhus University.
    4. Ole E. Barndorff-Nielsen & Mikko S. Pakkanen & Jürgen Schmiegel, 2013. "Assessing Relative Volatility/Intermittency/Energy Dissipation," CREATES Research Papers 2013-15, Department of Economics and Business Economics, Aarhus University.
    5. Mark Podolskij & Mathieu Rosenbaum, 2012. "Testing the local volatility assumption: a statistical approach," Annals of Finance, Springer, vol. 8(1), pages 31-48, February.
    6. Adam D. Bull, 2015. "Semimartingale detection and goodness-of-fit tests," Papers 1506.00088, arXiv.org, revised Jun 2016.
    7. Ramírez-Piscina, L. & Sancho, J.M., 2018. "Periodic spiking by a pair of ionic channels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 345-354.
    8. Duval, Céline & Luçon, Eric & Pouzat, Christophe, 2022. "Interacting Hawkes processes with multiplicative inhibition," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 180-226.
    9. Christensen, K. & Podolskij, M. & Thamrongrat, N. & Veliyev, B., 2017. "Inference from high-frequency data: A subsampling approach," Journal of Econometrics, Elsevier, vol. 197(2), pages 245-272.
    10. Christensen, Kim & Thyrsgaard, Martin & Veliyev, Bezirgen, 2019. "The realized empirical distribution function of stochastic variance with application to goodness-of-fit testing," Journal of Econometrics, Elsevier, vol. 212(2), pages 556-583.
    11. Dias, José Carlos & Vidal Nunes, João Pedro, 2018. "Universal recurrence algorithm for computing Nuttall, generalized Marcum and incomplete Toronto functions and moments of a noncentral χ2 random variable," European Journal of Operational Research, Elsevier, vol. 265(2), pages 559-570.
    12. Heesen, Sophie & Stannat, Wilhelm, 2021. "Fluctuation limits for mean-field interacting nonlinear Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 139(C), pages 280-297.
    13. Mark Podolskij & Daniel Ziggel, 2007. "A Range-Based Test for the Parametric Form of the Volatility in Diffusion Models," CREATES Research Papers 2007-26, Department of Economics and Business Economics, Aarhus University.
    14. Li, Yingying & Liu, Guangying & Zhang, Zhiyuan, 2022. "Volatility of volatility: Estimation and tests based on noisy high frequency data with jumps," Journal of Econometrics, Elsevier, vol. 229(2), pages 422-451.
    15. I.B., Tagne nkounga & F.M., Moukam kakmeni & R., Yamapi, 2022. "Birhythmic oscillations and global stability analysis of a conductance-based neuronal model under ion channel fluctuations," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    16. Peter Behl & Holger Dette & Manuel Frondel & Harald Tauchmann, 2011. "Being Focused: When the Purpose of Inference Matters for Model Selection," Ruhr Economic Papers 0264, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    17. Behl, Peter & Dette, Holger & Frondel, Manuel & Vance, Colin, 2019. "A focused information criterion for quantile regression: Evidence for the rebound effect," The Quarterly Review of Economics and Finance, Elsevier, vol. 71(C), pages 223-227.
    18. Chevallier, J. & Duarte, A. & Löcherbach, E. & Ost, G., 2019. "Mean field limits for nonlinear spatially extended Hawkes processes with exponential memory kernels," Stochastic Processes and their Applications, Elsevier, vol. 129(1), pages 1-27.
    19. Behl, Peter & Dette, Holger & Frondel, Manuel & Tauchmann, Harald, 2013. "Energy substitution: When model selection depends on the focus," Energy Economics, Elsevier, vol. 39(C), pages 233-238.
    20. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, 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:spapps:v:173:y:2024:i:c:s0304414924000784. 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.