Nonparametric inference on high-dimensional Hawkes processes

Abstract

We develop a new nonpararmetric estimator of branching ratio matrix for high-dimensional Hawkes processes with time-varying baseline intensity. In order to incorporate high-dimensionality, we first consider a PCA analysis in the first paper, and derive its theoretical properties. Then in the second paper, we develop a nonparametric branching ratio estimator which is robust to the time-varying baseline intensity under univariate setting. In the last paper, we develop a multi-variate version of nonparametric branching ratio estimator, and apply it to explaining the micro-foundation of Heston-type volatility model. We expect that our estimator would be used to causal analysis of the point processes under time-varying external intensity.