A Lagrangian multiplier test for market microstructure noise with applications to sampling interval determination for realized volatilities

A Lagrangian multiplier test is proposed for testing market microstructure noise (MMN) in financial asset prices. The test is very simple and is asymptotically chi-squared with 1-degree of freedom. The test is applied to sampling interval determination for realized volatilities (RVs) which validates the commonly used “ad hoc rule of between 5 and 30 min” for sampling interval. The proposed test gives a statistical justification for RVs of negligible serial correlation in the log-returns owning to MMN for sampling interval larger than a selected one. A Monte Carlo experiment shows reasonable size and power performance of the test. The proposed test is illustrated for two real data sets.