Mathematical Finance, Stochastic Analysis, and Machine Learning Seminar By Sam Cohen: Gradient Based Estimation of Linear Hawkes Processes
Sam Cohen, Mathematical Institute at Oxford University
Gradient Based Estimation of Linear Hawkes Processes
Linear multivariate Hawkes processes (MHP) are a fundamental class of point processes with self-excitation, common in finance, biology and other areas. 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.
Based on work with Alvaro Cartea and Saad Labyad (https://arxiv.org/abs/2111.10637)
Mathematical Finance, Stochastic Analysis, and Machine Learning