Gradient-based estimation of linear Hawkes processes with general kernels

51 Pages Posted: 23 Nov 2021

See all articles by Álvaro Cartea

Álvaro Cartea

University of Oxford; University of Oxford - Oxford-Man Institute of Quantitative Finance

Samuel N. Cohen

University of Oxford - Mathematical Institute; The Alan Turing Institute

Saad Labyad

University of Oxford - Mathematical Institute; University of Oxford - Oxford-Man Institute of Quantitative Finance

Date Written: November 22, 2021

Abstract

Linear multivariate Hawkes processes (MHP) are a fundamental class of point processes with self-excitation. When estimating parameters for these processes, a difficulty is that the two main error functionals, the log-likelihood and the least squares error (LSE), as well as the evaluation of their gradients, have a quadratic complexity in the number of observed events. In practice, this prohibits the use of exact gradient-based algorithms for parameter estimation. We construct an adaptive stratified sampling estimator of the gradient of the LSE. This results in a fast parametric estimation method for MHP with general kernels, applicable to large datasets, which compares favourably with existing methods.

Keywords: Hawkes processes, stochastic gradient descent, point processes, Monte Carlo methods, adaptive stratified sampling.

JEL Classification: C13, C14, C22

Suggested Citation

Cartea, Álvaro and Cohen, Samuel N. and Labyad, Saad, Gradient-based estimation of linear Hawkes processes with general kernels (November 22, 2021). Available at SSRN: https://ssrn.com/abstract=3969208 or http://dx.doi.org/10.2139/ssrn.3969208

Álvaro Cartea

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

Samuel N. Cohen

University of Oxford - Mathematical Institute ( email )

Woodstock Road
Oxford, Oxfordshire OX26GG
United Kingdom

The Alan Turing Institute ( email )

British Library
96 Euston Road
London, NW1 2DB
United Kingdom

Saad Labyad (Contact Author)

University of Oxford - Mathematical Institute ( email )

Radcliffe Observatory, Andrew Wiles Building
Woodstock Rd
Oxford, Oxfordshire OX2 6GG
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

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