Electronic Journal of Statistics

Nearly assumptionless screening for the mutually-exciting multivariate Hawkes process

Shizhe Chen, Daniela Witten, and Ali Shojaie

Full-text: Open access

Abstract

We consider the task of learning the structure of the graph underlying a mutually-exciting multivariate Hawkes process in the high-dimensional setting. We propose a simple and computationally inexpensive edge screening approach. Under a subset of the assumptions required for penalized estimation approaches to recover the graph, this edge screening approach has the sure screening property: with high probability, the screened edge set is a superset of the true edge set. Furthermore, the screened edge set is relatively small. We illustrate the performance of this new edge screening approach in simulation studies.

Article information

Source
Electron. J. Statist. Volume 11, Number 1 (2017), 1207-1234.

Dates
Received: September 2016
First available in Project Euclid: 11 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1491897620

Digital Object Identifier
doi:10.1214/17-EJS1251

Subjects
Primary: 60G55: Point processes
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62H12: Estimation

Keywords
Hawkes process screening high-dimensionality

Rights
Creative Commons Attribution 4.0 International License.

Citation

Chen, Shizhe; Witten, Daniela; Shojaie, Ali. Nearly assumptionless screening for the mutually-exciting multivariate Hawkes process. Electron. J. Statist. 11 (2017), no. 1, 1207--1234. doi:10.1214/17-EJS1251. https://projecteuclid.org/euclid.ejs/1491897620.


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