Estimation of an Order Book Dependent Hawkes Process for Large Datasets

ArXiv ID: 2307.09077 “View on arXiv”

Authors: Unknown

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.

Keywords: Hawkes process, High-frequency trading, Order book, Point process, Nonlinearity, Equities

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper presents a high-dimensional point process model with exponential kernels and non-linear covariate mappings (e.g., one-hot encoding), requiring advanced theoretical results on stationarity and convergence. It includes an application on NYSE stock data using a specific dataset (Lobster), a defined out-of-sample testing procedure, and discusses implementation challenges like quadratic programming, though it lacks full backtest code or live deployment details.

  flowchart TD
    A["Research Goal<br>Estimate Hawkes process with high dimensional<br>order book covariates for large datasets"] --> B["Data Input<br>Billions of data points<br>High-frequency trading events"]
    B --> C["Methodology<br>Point process with intensity:<br>Product of Hawkes process &<br>High dimensional covariate functions"]
    C --> D["Computation<br>Scalable algorithm for large datasets<br>Convergence & Consistency proofs"]
    D --> E["Testing<br>Out-of-sample test statistic<br>Assess model specifications"]
    E --> F["Application<br>4 NYSE stocks<br>Nonlinearity adds value to self-excitation"]
    F --> G["Key Outcomes<br>Stationarity conditions established<br>Nonlinearity captures order book dynamics"]