We propose methods to infer jumps of a semi-martingale, which describes long-term price dynamics based on discrete, noisy, high-frequency observations. Different to the classical model of additive, centered market microstructure noise, we consider one-sided microstructure noise for order prices in a limit order book. We develop methods to estimate, locate and test for jumps using local order statistics. We provide a local test and show that we can consistently estimate price jumps. The main contribution is a global test for jumps. We establish the asymptotic properties and optimality of this test. We derive the asymptotic distribution of a maximum statistic under the null hypothesis of no jumps based on extreme value theory. We prove consistency under the alternative hypothesis. The rate of convergence for local alternatives is determined and shown to be much faster than optimal rates for the standard market microstructure noise model. This allows the identification of smaller jumps. In the process, we establish uniform consistency for spot volatility estimation under one-sided microstructure noise. A simulation study sheds light on the finite-sample implementation and properties of our new statistics and draws a comparison to a popular method for market microstructure noise. We showcase how our new approach helps to improve jump detection in an empirical analysis of intra-daily limit order book data.

翻译：我们提出推断半鞅跳跃的方法，该方法基于离散、含噪的高频观测值描述长期价格动态。与经典的中心化市场微观结构加性噪声模型不同，我们考虑限价订单簿中订单价格的单侧微观结构噪声。我们开发了利用局部顺序统计量估计、定位和检验跳跃的方法。我们提供了一个局部检验，并证明能够一致地估计价格跳跃。主要贡献在于全局跳跃检验，我们建立了该检验的渐近性质与最优性。基于极值理论，我们推导出在无跳跃原假设下最大统计量的渐近分布，并证明其在备择假设下的一致性。我们确定了局部备择假设的收敛速度，该速度远快于标准市场微观结构噪声模型的最优速率，从而能够识别更小的跳跃。在此过程中，我们建立了单侧微观结构噪声下瞬时波动率估计的一致收敛性。仿真研究阐明了新统计量的有限样本实现与性质，并与一种流行的市场微观结构噪声方法进行了比较。通过日内限价订单簿数据的实证分析，我们展示了新方法如何提升跳跃检测效果。