Estimation of an Order Book Dependent Hawkes Process for Large Datasets

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. Large sample sizes can be common for high-frequency data applications using multiple instruments. Consistency results under weak conditions are established. 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. 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.