A ReMeDI for Microstructure Noise

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 finite moments of a microstructure noise process, which could be serially dependent and nonstationary, based on high-frequency data. We characterize the limit distributions of the proposed estimators and construct robust confidence intervals under infill asymptotics. We further demonstrate that the ReMeDI approach also works on low-frequency, non-infill data. It thus can be applied to many asset pricing and macroeconomic models, in which the time series have a permanent and a transitory component.We propose two liquidity measures that gauge the instantaneous and average bid-ask spread with potentially autocorrelated order flows. They can be consistently estimated within our framework. We provide an economic model to justify such measures as an intermediary's inventory risk measure when meeting serially dependent liquidity demand. Empirically we find our new liquidity measures are very effective to identify liquidity drains during the Flash Crash, when the market experienced extreme selling pressures