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.

翻译：提出了一种用于高频交易事件到达的点过程模型。其强度为霍克斯过程与源自订单簿的高维协变量函数的乘积。给出了该过程平稳性的条件。提出了一种即使在存在数十亿数据点的情况下也能估计该模型的算法，该算法可将协变量映射至高维空间。在使用多种流动性工具的高频数据应用中，大样本量较为常见。证明了算法的收敛性，建立了弱条件下的相合性结果，并提出了用于评估不同模型规范样本外性能的检验统计量。该方法被应用于纽约证券交易所（NYSE）交易的四种股票的研究。样本外检验程序表明，捕捉订单簿信息的非线性特征对高频交易事件的自激特性具有附加价值。