Statistical Methods in Finance 2022

June 28 to July 2, 2022


A tale of two time scales: Applications in Nonparametric Hawkes processes with Ito semimartingale Baseline

By Yoann Potiron
Keio University, Tokyo

In view of their tractability, Hawkes processes are widely employed in high-frequency data. However, even in the absence of kernel (i.e.\ Poisson case), it is well-documented empirically that the baseline is not constant, reproducing seasonalities from the financial market. In this paper, we relax this constancy assumption and consider a more realistic nonparametric framework where Hawkes self-exciting processes feature It\^o semimartingale with possible jumps as baseline. We are able to jointly and consistently estimate aggregated local Poisson estimates and truncated Two Scales Realized Volatility of these estimates, together with its central limit theory and feasible statistics. As a byproduct, we provide feasible limit theory of a nonparametric branching ratio (i.e.\ the $L^1$-norm of the kernel) estimator, the integrated baseline, the integrated volatility of the baseline and develop tests for the absence of Hawkes term, for a branching ratio level, for near criticality, for the absence of time-varying baseline, and for the absence of Brownian component in the baseline.