Trawl processes belong to the class of continuous-time, strictly stationary, infinitely divisible processes; they are defined as Levy bases evaluated over deterministic trawl sets. This article presents the first nonparametric estimator of the trawl function characterising the trawl set and the serial correlation of the process. Moreover, it establishes a detailed asymptotic theory for the proposed estimator, including a law of large numbers and a central limit theorem for various asymptotic relations between an in-fill and a long-span asymptotic regime. In addition, it develops consistent estimators for both the asymptotic bias and variance, which are subsequently used for establishing feasible central limit theorems which can be applied to data. A simulation study shows the good finite sample performance of the proposed estimators. The new methodology is applied to model misspecification testing, forecasting high-frequency financial spread data from a limit order book and to estimating the busy-time distribution of a stochastic queue.

翻译：拖网过程属于连续时间、严格平稳、无限可分过程类；它们被定义为在确定性拖网集上评估的Levy基。本文提出了首个用于表征拖网集及过程序列相关性的拖网函数非参数估计量。此外，文章为所提出的估计量建立了详细的渐近理论，包括针对填充渐近与长跨度渐近两种渐近机制间不同关系的强大数定律和中心极限定理。同时，本文还构建了渐近偏差与方差的一致估计量，并基于此建立了可用于实际数据的可行中心极限定理。模拟研究表明所提估计量具有良好的有限样本性能。新方法被应用于模型误设检验、限价订单簿高频金融价差数据预测，以及随机队列繁忙时间分布的估计。