粗糙噪声的微观结构基础
Microstructural Foundations of Rough Noise
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中文总结 AI 辅助
本文提出分离永久与短暂价格变动的微观结构模型，为粗糙噪声模型提供基础，开发GMM估计与检验，应用于2024年道琼斯成分股逐笔数据，发现粗糙噪声非普遍存在且具日际差异。
中文摘要 AI 辅助
近来有学者提出，用样本路径比标准布朗运动更粗糙的连续时间过程来建模价格中的微观结构噪声。本文针对逐笔价格变动提出一种微观结构模型，明确将永久价格变动与噪声导致的短暂价格变动分离。我们证明该模型如何收敛于永久价格过程的标准半鞅模型，加上源自宏观层面短暂价格变动的粗糙噪声项，为粗糙噪声模型提供了微观结构基础。随后，我们开发适用于逐笔数据的GMM估计方法，以及针对粗糙噪声的正式检验。通过模拟研究证明该估计量和检验在有限样本中有效，并将其应用于2024年道琼斯工业平均指数成分股的逐笔数据。由于我们的估计量专为逐笔数据设计，故在日度层面估计粗糙度，发现存在显著的日际差异。研究发现粗糙噪声虽存在但并非普遍：即使被检测到，粗糙度指数通常接近0，且在短期价格反转主导的日子里最为明显。
英文摘要
Recently, it has been proposed to model the microstructure noise in prices by a continuous-time process with continuous sample paths that are rougher than those of a standard Brownian motion. In this paper, we propose a microstructural model for the tick-by-tick price changes that explicitly separates the permanent price changes from the fleeting price changes due to noise. We show how this model converges to a standard semimartingale model for the permanent price process, plus a rough noise term originating from the fleeting price changes on the macro scale. This provides a microstructural foundation for the rough-noise model. We then develop a GMM estimation method applicable to tick-by-tick data, together with a formal test for rough noise. We show that the estimator and test work in finite samples through a simulation study, and apply them to tick-by-tick data on Dow Jones Industrial Average constituents in 2024. Because our estimator is designed for tick-by-tick data, we estimate roughness at the daily level, revealing substantial day-to-day variation. We find that rough noise, while present, is not universal: even when detected, the roughness index is typically close to zero, and it is most pronounced on days dominated by short-run price reversals.
