A ReMeDI for Microstructure Noise

Abstract

We introduce the Realized moMents of Disjoint Increments (ReMeDI) paradigm to measure microstructure noise (the deviation of the observed asset prices from the fundamental values caused by market imperfections). We propose consistent estimators of arbitrary moments of the microstructure noise process based on highfrequency data, where the noise process could be serially dependent, endogenous, and nonstationary. We characterize the limit distributions of the proposed estimators and construct confidence intervals under infill asymptotics. Our simulation and empirical studies show that the ReMeDI approach is very effective to measure the scale and the serial dependence of microstructure noise. Moreover, the estimators are quite robust to model specifications, sample sizes and data frequencies.

A ReMeDI for Microstructure Noise

“…Theoretically, the rounding model is difficult to work with in the very general semimartingale setting we have for the efficient price, and we have not so far managed to include this feature in our theoretical analysis. However, we do have simulation evidence suggesting that the ReMeDI estimator also works quite well in this case; see Section E.2 in Li and Linton (2022). Li and Mykland (2015) found that subsampling helps mitigate rounding errors.…”

“…Second, the ReMeDI approach works beyond the infill framework. Specifically, in the working paper version, Li and Linton (2019), we proved that the ReMeDI estimator is consistent and has an associated CLT in a long‐span, non‐infill setting. In this case, the method works provided the efficient price is a martingale, in which case its increments are uncorrelated at any horizon.…”

“…In the Supplemental Material (Li and Linton (2022)), we use the transaction prices of General Electric (GE) and Citigroup (Citi), and we obtain similar results.…”

“…The Supplemental Material (Li and Linton (2022)) provides additional simulation studies to examine the quality of the CLT approximation, the effect of rounding error due to the discreteness of price, and the sensitivity to the choice of tuning parameters.…”

“…where r(j; k n ) := E( kn j (χ) n 0 ). When k n satisfies the conditions specified in (17) of Li and Linton (2021), we write g(j) n i and u(j) n i instead of g(j k n ) n i and u(j k n ) n i . Following Jacod, Li, and Zheng (2017), we assume the processes X, α, α, γ and the observation times T n i are defined on a space ( (0) F (0) (F t ) t≥0 P (0) ); {χi}i∈Z is defined on another space ( (1) G (G i ) i∈Z P (1) ) with G i := σ (χ k : k ≤ i) and G i := σ (χ k : k ≥ i).…”