Mathematical Finance, Stochastic Analysis, and Machine Learning Seminar By Sam Cohen: Gradient Based Estimation of Linear Hawkes Processes
Speaker:
, Mathematical Institute at Oxford University
Title:
Gradient Based Estimation of Linear Hawkes Processes
Abstract:
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 ()
Mathematical Finance, Stochastic Analysis, and Machine Learning