ESTIMATION OF A HIGH-DIMENSIONAL COUNTING PROCESS WITHOUT PENALTY FOR HIGH-FREQUENCY EVENTS
提出一种无需模型惩罚或参数收缩的高维计数过程估计方法，用于高频交易中买卖订单到达的建模，并在原油期货市场实证中揭示订单簿形状和动态对交易到达的关键作用。
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.