On the nonparametric inference of coefficients of self-exciting jump-diffusion

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• dc.contributor.author Amorino, Chiara
• dc.contributor.author Dion-Blanc, Charlotte
• dc.contributor.author Gloter, Arnaud
• dc.contributor.author Lemler, Sarah
• dc.date.accessioned 2025-11-04T17:38:10Z
• dc.date.available 2025-11-04T17:38:10Z
• dc.date.issued 2022
• dc.date.updated 2025-11-04T17:38:09Z
• dc.description.abstract In this paper, we consider a one-dimensional diffusion process with jumps driven by a Hawkes process. We are interested in the estimations of the volatility function and of the jump function from discrete high-frequency observations in a long time horizon which remained an open question until now. First, we propose to estimate the volatility coefficient. For that, we introduce a truncation function in our estimation procedure that allows us to take into account the jumps of the process and estimate the volatility function on a linear subspace of L(A) whereA is a compact interval of R. We obtain a bound for the empirical risk of the volatility estimator, ensuring its consistency, and then we study an adaptive estimator w.r.t. the regularity. Then, we define an estimator of a sum between the volatility and the jump coefficient modified with the conditional expectation of the intensity of the jumps. We also establish a bound for the empirical risk for the non-adaptive estimators of this sum, the convergence rate up to the regularity of the true function, and an oracle inequality for the final adaptive estimator. Finally, we give a methodology to recover the jump function in some applications. We conduct a simulation study to measure our estimators accuracy in practice and discuss the possibility of recovering the jump function from our estimation procedure.
• dc.description.sponsorship C. Amorino gratefully acknowledges financial support of ERC Consolidator Grant 815703 "STAMFORD: Statistical Methods for High Dimensional Diffusions".
• dc.format.mimetype application/pdf
• dc.identifier.citation Amorino C, Dion-Blanc C, Gloter A, Lemler S. On the nonparametric inference of coefficients of self-exciting jump-diffusion. Electron J Stat. 2022;16(1):3212-77. DOI: 10.1214/22-EJS2019
• dc.identifier.doi http://dx.doi.org/10.1214/22-EJS2019
• dc.identifier.issn 1935-7524
• dc.identifier.uri http://hdl.handle.net/10230/71769
• dc.language.iso eng
• dc.publisher Institute of Mathematical Statistics
• dc.relation.ispartof Electronic Journal of Statistics. 2022;16(1):3212-3277
• dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/815703
• dc.rights Creative Commons Attribution 4.0 International License
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri http://creativecommons.org/licenses/by/4.0/
• dc.subject.keyword Jump diffusion
• dc.subject.keyword Hawkes process
• dc.subject.keyword Volatility estimation
• dc.subject.keyword Nonparametric estimation
• dc.subject.keyword Adaptation
• dc.title On the nonparametric inference of coefficients of self-exciting jump-diffusion
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion