Title: Nonparametric estimation of Hawkes branching ratio with Ito semimartingale baseline
Authors: Seunghyeon Yu - KAIST (Korea, South) [presenting]
Yoann Potiron - Keio University (Japan)
Abstract: 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. We relax this constancy assumption and consider a more realistic nonparametric framework where Hawkes's self-exciting processes feature Ito semimartingale with possible jumps as a baseline. Based on local Poisson estimates and Two Scales truncated Realized Volatility of these estimates, we are able to jointly and consistently estimate the integrated baseline, the integrated volatility of the baseline and the branching ratio, i.e. the L1-norm of the kernel, together with its central limit theory and feasible statistics. As a byproduct of the central limit theory, we develop tests for the presence of Hawkes term, for criticality, for the presence of a time-varying baseline, and for Brownian baseline. A simulation study corroborates the theory and documents the superiority of our branching ratio estimator over two concurrent methods in realistic configurations. An empirical study illustrates that our estimator can capture endogeneity and explain the volatility well with the micro-foundation-based relation.