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Sparse estimation for generalized exponential marked Hawkes process

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  • Masatoshi Goda

    (University of Tokyo
    CREST)

Abstract

We established a sparse estimation method for the generalized exponential marked Hawkes process by the penalized method to ordinary method (P–O) estimator. Furthermore, we evaluated the probability of the correct variable selection. In the course of this, we established a framework for a likelihood analysis and the P–O estimation when there might be nuisance parameters, and the true value of the parameter might be at the boundary of the parameter space. Finally, numerical simulations are given for several important examples.

Suggested Citation

  • Masatoshi Goda, 2023. "Sparse estimation for generalized exponential marked Hawkes process," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 139-169, April.
    • Handle: RePEc:spr:sistpr:v:26:y:2023:i:1:d:10.1007_s11203-022-09274-8
    DOI: 10.1007/s11203-022-09274-8
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    References listed on IDEAS

    as
    1. Masatoshi Goda, 2021. "Hawkes process and Edgeworth expansion with application to maximum likelihood estimator," Statistical Inference for Stochastic Processes, Springer, vol. 24(2), pages 277-325, July.
    2. Nakahiro Yoshida, 2011. "Polynomial type large deviation inequalities and quasi-likelihood analysis for stochastic differential equations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(3), pages 431-479, June.
    3. Clinet, Simon & Yoshida, Nakahiro, 2017. "Statistical inference for ergodic point processes and application to Limit Order Book," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 1800-1839.
    4. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    5. Simon Clinet, 2020. "Quasi-likelihood analysis for marked point processes and application to marked Hawkes processes," Papers 2001.11624, arXiv.org, revised Aug 2021.
    6. Marcello Rambaldi & Emmanuel Bacry & Fabrizio Lillo, 2017. "The role of volume in order book dynamics: a multivariate Hawkes process analysis," Quantitative Finance, Taylor & Francis Journals, vol. 17(7), pages 999-1020, July.
    7. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    8. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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