Starting from a basic model in which the dynamic of the transaction prices is a geometric Brownian motion disrupted by a microstructure white noise, corresponding to the random alternation of bids and asks, we propose moment-based estimators along with their statistical properties. We then make the model more realistic by considering serial dependence: we assume a geometric fractional Brownian motion for the price, then an Ornstein-Uhlenbeck process for the microstructure noise. In these two cases of serial dependence, we propose again consistent and asymptotically normal estimators. All our estimators are compared on simulated data with existing approaches, such as Roll, Corwin-Schultz, Abdi-Ranaldo, or Ardia-Guidotti-Kroencke estimators.

翻译：从一个基础模型出发，其中交易价格的动态过程是一个受微观结构白噪声干扰的几何布朗运动，该噪声对应于买卖报价的随机交替，我们提出了基于矩的估计量及其统计性质。随后，我们通过考虑序列依赖性使模型更贴近现实：我们假设价格服从几何分数布朗运动，进而假设微观结构噪声服从奥恩斯坦-乌伦贝克过程。在这两种序列依赖性的情况下，我们再次提出了一致且渐近正态的估计量。我们所有的估计量均在模拟数据上与现有方法（如Roll、Corwin-Schultz、Abdi-Ranaldo或Ardia-Guidotti-Kroencke估计量）进行了比较。