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Hawkes process and Edgeworth expansion with application to maximum likelihood estimator

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  • Masatoshi Goda

    (University of Tokyo
    CREST)

Abstract

We provide a rigorous mathematical foundation of the theory for the higher-order asymptotic behavior of the one-dimensional Hawkes process with an exponential kernel. As an important application, we give the second-order asymptotic distribution for the maximum likelihood estimator of the exponential Hawkes process.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sistpr:v:24:y:2021:i:2:d:10.1007_s11203-021-09237-5
    DOI: 10.1007/s11203-021-09237-5
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    References listed on IDEAS

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    1. Vladimir Filimonov & Didier Sornette, 2012. "Quantifying Reflexivity in Financial Markets: Towards a Prediction of Flash Crashes," Swiss Finance Institute Research Paper Series 12-02, Swiss Finance Institute.
    2. Abergel,Frédéric & Anane,Marouane & Chakraborti,Anirban & Jedidi,Aymen & Muni Toke,Ioane, 2016. "Limit Order Books," Cambridge Books, Cambridge University Press, number 9781107163980.
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    4. Frédéric Abergel & Anirban Chakraborti & Aymen Jedidi & Ioane Muni Toke & Marouane Anane, 2016. "Limit Order Books," Post-Print hal-02177394, HAL.
    5. Vladimir Filimonov & Didier Sornette, 2012. "Quantifying reflexivity in financial markets: towards a prediction of flash crashes," Papers 1201.3572, arXiv.org, revised Apr 2012.
    6. Yuji Sakamoto & Nakahiro Yoshida, 2004. "Asymptotic expansion formulas for functionals of ε-Markov processes with a mixing property," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(3), pages 545-597, September.
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    Cited by:

    1. Tudor, Ciprian A. & Yoshida, Nakahiro, 2023. "High order asymptotic expansion for Wiener functionals," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 443-492.
    2. Masatoshi Goda, 2023. "Sparse estimation for generalized exponential marked Hawkes process," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 139-169, April.

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