论文标题
拖网过程的非参数估计：理论和应用
Nonparametric estimation of trawl processes: Theory and Applications
论文作者
论文摘要
拖网过程属于连续时间的类别，严格固定，无限划分的过程；它们被定义为在确定性拖网组中评估的莱维基地。本文介绍了拖网函数的第一个非参数估计器，该函数表征了拖网集和该过程的串行相关性。此外，它为提出的估计量建立了详细的渐近理论，包括大数量定律和一个中心限制定理，用于填充和长跨渐近渐近状态之间的各种渐近关系。此外，它为渐近偏差和方差开发一致的估计量，随后用于建立可应用的可行中心极限定理，可以应用于数据。一项仿真研究显示了拟议估计器的良好有限样本性能。新方法应用于从限制订单簿中预测高频财务扩散数据，并估计随机队列的繁忙时间分布。
Trawl processes belong to the class of continuous-time, strictly stationary, infinitely divisible processes; they are defined as Lévy 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 forecasting high-frequency financial spread data from a limit order book and to estimating the busy-time distribution of a stochastic queue.
