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This paper introduces a simple and intuitive measure of microstructure noise, the deviation of observable transaction prices from fundamental values. We measure the moments of noise, in particular, the variances and autocovariances under a general nonparametric setting. We demonstrate the intrinsic consistency of the proposed estimators without restrictions on data frequencies, and characterize the limit distributions under infill asymptotics. Simulation studies show the robustness of the proposed estimators to data frequencies and model specifications.
The new econometric techniques provide two liquidity measures that gauge the instantaneous and average bid-ask spread with potentially autocorrelated order flows. While being flexible with the autocorrelation structures, the new estimators only employ the transaction prices thus do not require any knowledge of the order flows. Empirically we find that microstructure noise in transaction data tends to be positively autocorrelated. Such positive autocorrelation induces sharp discrepancies among the bid-ask spread measures: The average measures are persistently larger than the instantaneous ones, whereas the classic Roll measures are further downward biased. Moreover, the intraday spreads have a prominent $L$-shape: The magnitude is much larger at the beginning of the trading day, and it is associated with extremely large transactions.
