Estimation of an Order Book Dependent Hawkes Process for Large Datasets

TL;DR

This paper introduces a scalable Hawkes process model incorporating order book covariates for high frequency trading data, with proven convergence, consistency, and out-of-sample testing.

Contribution

It develops a novel estimation algorithm capable of handling billions of data points and high-dimensional covariates in high frequency trading.

Findings

Capturing nonlinearity in order book data improves model performance.

The algorithm converges and is consistent under weak conditions.

Out-of-sample tests show added value of nonlinear order book features.

Abstract

A point process for event arrivals in high frequency trading is presented. The intensity is the product of a Hawkes process and high dimensional functions of covariates derived from the order book. Conditions for stationarity of the process are stated. An algorithm is presented to estimate the model even in the presence of billions of data points, possibly mapping covariates into a high dimensional space. The large sample size can be common for high frequency data applications using multiple liquid instruments. Convergence of the algorithm is shown, consistency results under weak conditions is established, and a test statistic to assess out of sample performance of different model specifications is suggested. The methodology is applied to the study of four stocks that trade on the New York Stock Exchange (NYSE). The out of sample testing procedure suggests that capturing the nonlinearity of the order book information adds value to the self exciting nature of high frequency trading events.