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Title: Nonparametric inference of coefficients of self-exciting jump-diffusion processes Authors:  Chiara Amorino - Universite du Luxembourg (Luxembourg)
Charlotte Dion - Sorbonne Universite (France)
Arnaud Gloter - Universite d Evry Val d Essonne (France) [presenting]
Sarah Sarah Lemler - Ecole CentraleSupelec (France)
Abstract: A one-dimensional diffusion process with jumps driven by a Hawkes process is considered. 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. We first 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 $L^2(A)$ where $A$ is a compact interval of $\mathbb{R}$. We obtain a bound for the empirical risk of the volatility estimator and establish an oracle inequality for the adaptive estimator to measure the performance of the procedure. Then, we propose 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 and an oracle inequality for the final adaptive estimator.