Statistical Properties of Microstructure Noise
Jean Jacod, Yingying Li, and Xinghua Zheng
TL;DR
This paper develops consistent estimators for moments and auto-correlations of microstructure noise, with theoretical guarantees and empirical validation, enhancing understanding of noise properties in financial data.
Contribution
It introduces new estimators for moments and auto-correlations of microstructure noise, with proven consistency and asymptotic normality, applicable even with jumps and irregular sampling.
Findings
Estimators perform well in simulations with jumps and irregular times.
Empirical evidence shows positive auto-correlation in stock microstructure noise.
The methods improve understanding of noise structure in high-frequency data.
Abstract
We study the estimation of moments and joint moments of microstructure noise. Estimators of arbitrary order of (joint) moments are provided, for which we establish consistency as well as central limit theorems. In particular, we provide estimators of auto-covariances and auto-correlations of the noise. Simulation studies demonstrate excellent performance of our estimators even in the presence of jumps and irregular observation times. Empirical studies reveal (moderate) positive auto-correlation of the noise for the stocks tested.
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Taxonomy
TopicsFinancial Risk and Volatility Modeling · Forecasting Techniques and Applications · Complex Systems and Time Series Analysis