Non-parametric kernel estimation for symmetric Hawkes processes. Application to high frequency financial data

TL;DR

This paper introduces a non-parametric numerical method to estimate kernel functions in symmetric multivariate Hawkes processes, with applications to high-frequency financial data revealing long memory effects.

Contribution

The paper develops a novel non-parametric estimation technique based on second order statistics for symmetric Hawkes processes, applicable to financial microstructure data.

Findings

Kernel shapes exhibit power-law decay indicating long memory.

Method effectively estimates kernels from high-frequency data.

Empirical analysis confirms long-range self-excitation in price dynamics.

Abstract

We define a numerical method that provides a non-parametric estimation of the kernel shape in symmetric multivariate Hawkes processes. This method relies on second order statistical properties of Hawkes processes that relate the covariance matrix of the process to the kernel matrix. The square root of the correlation function is computed using a minimal phase recovering method. We illustrate our method on some examples and provide an empirical study of the estimation errors. Within this framework, we analyze high frequency financial price data modeled as 1D or 2D Hawkes processes. We find slowly decaying (power-law) kernel shapes suggesting a long memory nature of self-excitation phenomena at the microstructure level of price dynamics.