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

•A Lagrangian multiplier test is developed for market micro structure noise of financial asset prices.•The test is computationally very simple and has simple chi-square limiting null distribution.•The test is useful for determining sampling intervals 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.