Peter Korsbakke Christensen, Anders Midtgaard Norlyk
arXiv 31 Jul 2026 · Econometrics
arXiv:2607.29442 · PDF · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Carsten H. Chong and Thomas Delerue and Guoying Li (2025) When Frictions Are Fractional: Rough Noise in High-Frequency Data | 1.000 | 12 | 5 | 100% |
| 2 | Aït-Sahalia, Yacine and Yu, Jialin (2009) High frequency market microstructure noise estimates and liquidity measures | 1.000 | 7 | 3 | 100% |
| 3 | Shephard, Neil and Yang, Justin J (2017) Continuous time analysis of fleeting discrete price moves | 1.000 | 5 | 4 | 100% |
| 4 | El Euch, Omar and Fukasawa, Masaaki and Rosenbaum, Mathieu (2018) The microstructural foundations of leverage effect and rough volatility | 0.874 | 5 | 2 | 100% |
| 5 | Barndorff-Nielsen, \Ole Eiler\ and Hansen, \P. Reinhard\ and Asger L… (2009) Realized kernels in practice: trades and quotes | 0.737 | 3 | 2 | 100% |
| 6 | Andrews, Donald W K (2002) Generalized method of moments estimation when a parameter is on a boundary | 0.644 | 2 | 2 | 100% |
| 7 | Hasbrouck, J (2007) Empirical Market Microstructure: The Institutions, Economics, and Econometrics of Securities Trading | 0.644 | 2 | 2 | 100% |
| 8 | Jacod, Jean and Li, Yingying and Zheng, Xinghua (2017) Statistical Properties of Microstructure Noise | 0.644 | 2 | 2 | 100% |
| 9 | Roll, Richard (1984) A simple implicit measure of the effective bid-ask spread in an efficient market | 0.644 | 2 | 2 | 100% |
| 10 | Yacine Aït-Sahalia and Per A. Mykland and Lan Zhang (2011) Ultra high frequency volatility estimation with dependent microstructure noise | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 38 scored citations.