IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v83y2013i3p885-890.html
   My bibliography  Save this article

Moderate deviations for Hawkes processes

Author

Listed:
  • Zhu, Lingjiong

Abstract

In this paper, we obtain a moderate deviation principle for a class of point processes, i.e. linear Hawkes processes.

Suggested Citation

  • Zhu, Lingjiong, 2013. "Moderate deviations for Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 885-890.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:3:p:885-890
    DOI: 10.1016/j.spl.2012.12.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212004609
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2012.12.011?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. Bowsher, Clive G., 2007. "Modelling security market events in continuous time: Intensity based, multivariate point process models," Journal of Econometrics, Elsevier, vol. 141(2), pages 876-912, December.
    2. BAUWENS, Luc & HAUTSCH, Nikolaus, 2006. "Modelling financial high frequency data using point processes," LIDAM Discussion Papers CORE 2006080, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Chen, Xia, 2001. "Moderate deviations for Markovian occupation times," Stochastic Processes and their Applications, Elsevier, vol. 94(1), pages 51-70, July.
    4. Gusto Gaelle & Schbath Sophie, 2005. "FADO: A Statistical Method to Detect Favored or Avoided Distances between Occurrences of Motifs using the Hawkes' Model," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-28, September.
    5. V. Chavez-Demoulin & A. C. Davison & A. J. McNeil, 2005. "Estimating value-at-risk: a point process approach," Quantitative Finance, Taylor & Francis Journals, vol. 5(2), pages 227-234.
    6. Large, Jeremy, 2007. "Measuring the resiliency of an electronic limit order book," Journal of Financial Markets, Elsevier, vol. 10(1), pages 1-25, February.
    7. Gao, Fu-Qing, 1996. "Moderate deviations for martingales and mixing random processes," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 263-275, February.
    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. Selvamuthu, Dharmaraja & Pandey, Shamiksha & Tardelli, Paola, 2023. "Limit Theorems for an extended inverse Hawkes process with general exciting functions," Statistics & Probability Letters, Elsevier, vol. 197(C).
    2. Gao, Xuefeng & Zhu, Lingjiong, 2018. "Limit theorems for Markovian Hawkes processes with a large initial intensity," Stochastic Processes and their Applications, Elsevier, vol. 128(11), pages 3807-3839.
    3. Seol, Youngsoo, 2017. "Limit theorems for the compensator of Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 165-172.
    4. Lingjiong Zhu, 2015. "A State-Dependent Dual Risk Model," Papers 1510.03920, arXiv.org, revised Feb 2023.
    5. Seol, Youngsoo, 2019. "Limit theorems for an inverse Markovian Hawkes process," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    6. Xuefeng Gao & Lingjiong Zhu, 2018. "Functional central limit theorems for stationary Hawkes processes and application to infinite-server queues," Queueing Systems: Theory and Applications, Springer, vol. 90(1), pages 161-206, October.
    7. Kim, Gunhee & Choe, Geon Ho, 2019. "Limit properties of continuous self-exciting processes," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    8. Gao, Fuqing & Zhu, Lingjiong, 2018. "Some asymptotic results for nonlinear Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4051-4077.
    9. Behzad Mehrdad & Lingjiong Zhu, 2014. "On the Hawkes Process with Different Exciting Functions," Papers 1403.0994, arXiv.org, revised Sep 2017.
    10. Seol, Youngsoo, 2015. "Limit theorems for discrete Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 223-229.
    11. Youngsoo Seol, 2023. "Large Deviations for Hawkes Processes with Randomized Baseline Intensity," Mathematics, MDPI, vol. 11(8), pages 1-10, April.
    12. Youngsoo Seol, 2022. "Non-Markovian Inverse Hawkes Processes," Mathematics, MDPI, vol. 10(9), pages 1-12, April.

    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. Wheatley, Spencer & Filimonov, Vladimir & Sornette, Didier, 2016. "The Hawkes process with renewal immigration & its estimation with an EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 120-135.
    2. Filimonov, Vladimir & Bicchetti, David & Maystre, Nicolas & Sornette, Didier, 2014. "Quantification of the high level of endogeneity and of structural regime shifts in commodity markets," Journal of International Money and Finance, Elsevier, vol. 42(C), pages 174-192.
    3. Anatoliy Swishchuk & Aiden Huffman, 2020. "General Compound Hawkes Processes in Limit Order Books," Risks, MDPI, vol. 8(1), pages 1-25, March.
    4. repec:hal:wpaper:hal-00777941 is not listed on IDEAS
    5. Clements, Adam & Liao, Yin, 2017. "Forecasting the variance of stock index returns using jumps and cojumps," International Journal of Forecasting, Elsevier, vol. 33(3), pages 729-742.
    6. Volodymyr Korniichuk, 2012. "Forecasting extreme electricity spot prices," Cologne Graduate School Working Paper Series 03-14, Cologne Graduate School in Management, Economics and Social Sciences.
    7. Angelos Dassios & Hongbiao Zhao, 2017. "A Generalized Contagion Process With An Application To Credit Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-33, February.
    8. Adam Clements & Yin Liao, 2014. "The role in index jumps and cojumps in forecasting stock index volatility: Evidence from the Dow Jones index," NCER Working Paper Series 101, National Centre for Econometric Research.
    9. Dassios, Angelos & Jang, Jiwook & Zhao, Hongbiao, 2019. "A generalised CIR process with externally-exciting and self-exciting jumps and its applications in insurance and finance," LSE Research Online Documents on Economics 102043, London School of Economics and Political Science, LSE Library.
    10. Ioane Muni Toke, 2010. ""Market making" behaviour in an order book model and its impact on the bid-ask spread," Papers 1003.3796, arXiv.org, revised Jun 2010.
    11. Jang, Jiwook & Dassios, Angelos, 2013. "A bivariate shot noise self-exciting process for insurance," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 524-532.
    12. Maxime Morariu-Patrichi & Mikko Pakkanen, 2018. "State-dependent Hawkes processes and their application to limit order book modelling," CREATES Research Papers 2018-26, Department of Economics and Business Economics, Aarhus University.
    13. Maxime Morariu-Patrichi & Mikko S. Pakkanen, 2018. "State-dependent Hawkes processes and their application to limit order book modelling," Papers 1809.08060, arXiv.org, revised Sep 2021.
    14. Ioane Muni Toke, 2011. ""Market making" behaviour in an order book model and its impact on the bid-ask spread," Post-Print hal-01705266, HAL.
    15. Anatoliy Swishchuk, 2017. "General Compound Hawkes Processes in Limit Order Books," Papers 1706.07459, arXiv.org, revised Jun 2017.
    16. Adam E Clements & Yin Liao, 2013. "Modeling and forecasting realized volatility: getting the most out of the jump component," NCER Working Paper Series 93, National Centre for Econometric Research.
    17. Kyungsub Lee, 2022. "Application of Hawkes volatility in the observation of filtered high-frequency price process in tick structures," Papers 2207.05939, arXiv.org, revised Sep 2024.
    18. Ban Zheng & François Roueff & Frédéric Abergel, 2014. "Ergodicity and scaling limit of a constrained multivariate Hawkes process," Post-Print hal-00777941, HAL.
    19. Steffen Volkenand & Günther Filler & Martin Odening, 2020. "Price Discovery and Market Reflexivity in Agricultural Futures Contracts with Different Maturities," Risks, MDPI, vol. 8(3), pages 1-17, July.
    20. Anatoliy Swishchuk & Aiden Huffman, 2018. "General Compound Hawkes Processes in Limit Order Books," Papers 1812.02298, arXiv.org.
    21. Angelos Dassios & Jiwook Jang & Hongbiao Zhao, 2019. "A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and Its Applications in Insurance and Finance," Risks, MDPI, vol. 7(4), pages 1-18, October.

    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:83:y:2013:i:3:p:885-890. 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.