# Analysis of order book flows using a nonparametric estimation of the branching ratio matrix

## TL;DR

This paper presents a fast nonparametric method for estimating the branching ratio matrix of multivariate Hawkes processes, applied to high-frequency order book data to uncover relationships between order events across assets.

## Contribution

It introduces a novel nonparametric estimation technique for the branching ratio matrix of multivariate Hawkes processes, enabling efficient analysis of high-frequency order book data.

## Key findings

- Successfully applied to EUREX order book data
- Revealed relationships between order events within and across assets
- Scalable to multi-asset high-frequency data

## Abstract

We introduce a new non parametric method that allows for a direct, fast and efficient estimation of the matrix of kernel norms of a multivariate Hawkes process, also called branching ratio matrix. We demonstrate the capabilities of this method by applying it to high-frequency order book data from the EUREX exchange. We show that it is able to uncover (or recover) various relationships between all the first level order book events associated with some asset when mapped to a 12-dimensional process. We then scale up the model so as to account for events on two assets simultaneously and we discuss the joint high-frequency dynamics.