64th ISI World Statistics Congress - Ottawa, Canada

64th ISI World Statistics Congress - Ottawa, Canada

Nonparametric inference of coefficients of self-exciting jump-diffusion processes

Author

AG
Arnaud Gloter

Co-author

  • C
    Chiara Amorino
  • C
    Charlotte Dion
  • S
    Sarah Lemler

Conference

64th ISI World Statistics Congress - Ottawa, Canada

Format: IPS Abstract

Keywords: hawkes, nonparametric, processes

Abstract

I will present nonparametric inference of the coefficients of a self-exciting jump-diffusion process based on high-frequency observations over a long-time horizon. The proposed inference procedure consists of three steps: first, the volatility coefficient is estimated over an appropriate linear subspace through a smoothed truncation methodology. A theoretical bound for the empirical risk is obtained, making a regularity-based adaptive estimation possible subsequently. Second, an estimator of a sum between the volatility and the coefficient of self-exciting jumps is obtained through the conditional expectation of the jump intensity. Therein, an oracle inequality for an adaptive estimator is obtained. Finally, a methodology is given to recover the jump-component function. Extensive simulation studies are conducted to measure the accuracy of the proposed estimators in practice. This is a joint work with C. Amorino (Université du Luxembourg), C. Dion (Sorbonne Université), S. Lemler (Ecole CentraleSupelec)