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

“…where s k n j, j ; k := s 0 j, j ; k + s 1 j, j ; k + s 2,k n j, j ; k , and s 0 (j, j ; k) , s 1 (j, j ; k) are introduced in Appendix B.1 in Li and Linton (2020).…”

“…We assume k n satisfies (14) in Li and Linton (2020). The methodology introduced here can also be applied to other choices of k n , e.g., k n specified in (12).…”

“…The estimators seem quite complicated. However, the intuition will be clear in light of the following convergences, which are proved in the supplementary material Li and Linton (2020):…”

“…The supplementary material Li and Linton (2020) provides additional simulation studies to examine the CLT, the effect of rounding error due to the discreteness of price and sensitivity to the choice of tuning parameters. •10 −7…”

“…We examine the feasible CLT presented in (21) of Li and Linton (2020) for = 0, 1, 2. The QQ-plots in Figure E.1 clearly support the limit distribution.…”