Inference for calendar effects in microstructure noise
提出了一个统计推断方法，用于分析高频数据中微观结构噪声的日历效应，首次在一般半鞅加噪声框架下建立了理论，并通过实证发现中国股票噪声日历效应随时间显著变化，而标普500期货则保持稳定。
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.