Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 62, Issue 4, Pages 2184-2202Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2016.2533397
Keywords
Stochastic processes; covariance matrices; estimation; microstructure; earthquakes; inverse problems; discrete-event systems; multivariate point processes
Funding
- chair Financial Risks of the Risk Foundation
- chair Mutating Markets of the French Federation of Banks
- chair Quantitative Management Initiative of Quant Vallet/Risk Foundation
Ask authors/readers for more resources
We show that the jumps correlation matrix of a multivariate Hawkes process is related to the Hawkes kernel matrix through a system of Wiener-Hopf integral equations. A Wiener-Hopf argument allows one to prove that this system (in which the kernel matrix is the unknown) possesses a unique causal solution and consequently that the first-and second-order properties fully characterize a Hawkes process. The numerical inversion of this system of integral equations allows us to propose a fast and efficient method, which main principles were initially sketched by Bacry and Muzy, to perform a non-parametric estimation of the Hawkes kernel matrix. In this paper, we perform a systematic study of this non-parametric estimation procedure in the general framework of marked Hawkes processes. We precisely describe this procedure step by step. We discuss the estimation error and explain how the values for the main parameters should be chosen. Various numerical examples are given in order to illustrate the broad possibilities of this estimation procedure ranging from monovariate (power-law or non-positive kernels) up to three-variate (circular dependence) processes. A comparison with other non-parametric estimation procedures is made. Applications to high-frequency trading events in financial markets and to earthquakes occurrence dynamics are finally considered.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available