2026-04-14T05:31:55Zhttps://recercat.cat/oai/request

oai:recercat.cat:10230/717692025-11-05T19:02:53Zcom_2072_6col_2072_452952

2025-11-05T19:02:53Z urn:hdl:10230/71769 On the nonparametric inference of coefficients of self-exciting jump-diffusion Amorino, Chiara Dion-Blanc, Charlotte Gloter, Arnaud Lemler, Sarah Jump diffusion Hawkes process Volatility estimation Nonparametric estimation Adaptation 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. C. Amorino gratefully acknowledges financial support of ERC Consolidator Grant 815703 "STAMFORD: Statistical Methods for High Dimensional Diffusions". 2025-11-05T19:02:53Z 2025-11-05T19:02:53Z 2025-11-04T17:38:10Z 2025-11-04T17:38:10Z 2022 2025-11-04T17:38:09Z info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://hdl.handle.net/10230/71769 Electronic Journal of Statistics. 2022;16(1):3212-3277 info:eu-repo/grantAgreement/EC/H2020/815703 Creative Commons Attribution 4.0 International License http://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess Institute of Mathematical Statistics