This paper introduces a counting process for event arrivals in high-frequency trading, based on high-dimensional covariates. The novelty is that, under sparsity conditions on the true model, we do not need to impose any model penalty or parameters shrinkage, unlike Lasso. The procedure allows us to derive a central limit theorem to test restrictions in a two-stage estimator. We achieve this by the use of a sign constraint on the intensity which necessarily needs to be positive. In particular, we introduce an additive model to extract the nonlinear impact of order book variables on buy and sell trade arrivals. In the empirical application, we show that the shape and dynamics of the order book are fundamental in determining the arrival of buy and sell trades in the crude oil futures market. We establish our empirical results mapping the covariates into a higher-dimensional space. Consistently with the theoretical results, the estimated models are sparse in the number of parameters. Using this approach, we are also able to compare competing model hypotheses on the basis of an out-of-sample likelihood ratio type of test.

本文介绍了一种基于高维协变量的高频交易中事件到达的计数过程。新颖之处在于，在真实模型的稀疏条件下，我们不需要像 Lasso 那样施加任何模型惩罚或参数收缩。该过程使我们能够导出中心极限定理来测试两阶段估计器中的限制。我们通过对强度使用符号约束来实现这一点，该强度必须为正。特别是，我们引入了一个附加模型来提取订单簿变量对买卖交易到达的非线性影响。在实证应用中，我们表明订单簿的形状和动态对于决定原油期货市场买卖交易的到来至关重要。我们建立了将协变量映射到更高维空间的经验结果。与理论结果一致，估计模型的参数数量稀疏。使用这种方法，我们还能够基于样本外似然比类型的测试来比较竞争模型假设。