非同步数据的超前-滞后参数估计
Estimation of the lead-lag parameter from non-synchronous data
摘要：
我们提出了一个简单的连续时间模型来模拟两个金融资产之间的超前滞后效应。二维过程$(X_t,Y_t)$再现超前-滞后效应，如果对于某个时移$\vartheta\in \mathbb{R}$，过程$(X_t,Y_{t+\vartheta})$是关于某个过滤的半鞅。时移$\vartheta$的值是超前-滞后参数。根据基础过滤，标准的无套利情况下，获得$\vartheta=0$。本文研究了在随机抽样的非同步数据下，未知参数$\vartheta\in \mathbb{R}$的估计问题，给出了$(X_t)$和$(Y_t)$的非同步数据.通过应用一定的对比度优化的基础上的修改版本的Hayashi-Yoshida协变估计，我们得到了一致的估计的领先滞后参数，连同显式的收敛速率由抽样设计的稀疏性。
英文摘要：
We propose a simple continuous time model for modeling the lead-lag effect between two financial assets. A two-dimensional process $(X_t,Y_t)$ reproduces a lead-lag effect if, for some time shift $\vartheta\in \mathbb{R}$, the process $(X_t,Y_{t+\vartheta})$ is a semi-martingale with respect to a certain filtration. The value of the time shift $\vartheta$ is the lead-lag parameter. Depending on the underlying filtration, the standard no-arbitrage case is obtained for $\vartheta=0$. We study the problem of estimating the unknown parameter $\vartheta\in \mathbb{R}$, given randomly sampled non-synchronous data from $(X_t)$ and $(Y_t)$. By applying a certain contrast optimization based on a modified version of the Hayashi-Yoshida covariation estimator, we obtain a consistent estimator of the lead-lag parameter, together with an explicit rate of convergence governed by the sparsity of the sampling design.
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