🤖 AI Summary
This study addresses the decomposition of permanent price movements from transient microstructure noise using tick-by-tick transaction data and provides a microstructural foundation for rough noise observed at macroscopic scales. To this end, the authors develop a structural microstructure model that explicitly distinguishes between these two components and demonstrate its weak convergence to a semimartingale with a rough noise term in the macroscopic limit. This work establishes, for the first time, a microfounded theoretical basis for rough noise models grounded in high-frequency data, revealing their non-universality and pronounced intraday variability. Employing generalized method of moments (GMM) estimation coupled with formal statistical tests—validated through simulations to perform well in finite samples—the empirical analysis of 2024 Dow Jones constituents shows that rough noise is statistically significant only on days dominated by short-term price reversals, with estimated roughness exponents typically near zero.
📝 Abstract
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.