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Parametric estimation of Hawkes processes based on ordinary least squares

  • Benjamin Poignard
  • Yoann Potiron
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Abstract

We develop a parametric estimation framework for self-exciting Hawkes processes whose intensity functions admit a parametric form. The estimation procedure is based on ordinary least squares. To apply the least squares estimation, we restrict to a kernel class that can be expressed as a sum of the product of a parameter and a function. We first establish the central limit theorem for the proposed estimator. We then show the consistency of the asymptotic variance estimator. Finally, we introduce a Wald test statistic and derive its asymptotic distribution. We apply the proposed methodology to trade times from high-frequency financial asset data. Our empirical results provide evidence for three heterogeneous trader types. In particular, we identify two trader types as high-frequency traders and one trader type as fundamental trader.

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Cite

BibTeXRIS
BibTeX
@misc{poignard2026parametric,
  title = {{Parametric estimation of Hawkes processes based on ordinary least squares}},
  author = {Benjamin Poignard and Yoann Potiron},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03696},
  eprint = {2609.03696},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03696},
}
RIS
TY  - UNPB
TI  - Parametric estimation of Hawkes processes based on ordinary least squares
AU  - Benjamin Poignard
AU  - Yoann Potiron
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.03696
UR  - https://arxiv.org/abs/2609.03696
AB  - We develop a parametric estimation framework for self-exciting Hawkes processes whose intensity functions admit a parametric form. The estimation procedure is based on ordinary least squares. To apply the least squares estimation, we restrict to a kernel class that can be expressed as a sum of the product of a parameter and a function. We first establish the central limit theorem for the proposed estimator. We then show the consistency of the asymptotic variance estimator. Finally, we introduce a Wald test statistic and derive its asymptotic distribution. We apply the proposed methodology to trade times from high-frequency financial asset data. Our empirical results provide evidence for three heterogeneous trader types. In particular, we identify two trader types as high-frequency traders and one trader type as fundamental trader.
ER  -