Inference for calendar effects in microstructure noise

We develop a statistical inference procedure for the ubiquitous calendar effects in microstructure noise using high frequency data. This is, to the best of our knowledge, the first inference theory ever built for noise calendar effect under the general semi-martingale-plus-noise setup for prices contaminated with non-stationary, endogenous, and serially dependent microstructure noise. We devise a noise-calendar-effect estimator by an appropriately scaled average of high-frequency returns that precede a time of day across a large number of trading days. Feasible central limit theorem for the estimator is established under a joint infill and long-span asymptotics. Monte Carlo simulations corroborate our theoretical findings. An empirical study on the high-frequency data of the e-mini S&P 500 futures and a Chinese stock demonstrates that the noise calendar effect has undergone significant changes over time for the latter, yet remains stable for the former.