When Moving‐Average Models Meet High‐Frequency Data: Uniform Inference on Volatility
研究在噪声高频交易数据中估计波动率的方法，假设价格受移动平均噪声污染，通过最大化误设的移动平均模型似然来估计，并保证推断在多种噪声结构下统一有效。
We conduct inference on volatility with noisy high‐frequency data. We assume the observed transaction price follows a continuous‐time Itô‐semimartingale, contaminated by a discrete‐time moving‐average noise process associated with the arrival of trades. We estimate volatility, defined as the quadratic variation of the semimartingale, by maximizing the likelihood of a misspecified moving‐average model, with its order selected based on an information criterion. Our inference is uniformly valid over a large class of noise processes whose magnitude and dependence structure vary with sample size. We show that the convergence rate of our estimator dominates n 1/4 as noise vanishes, and is determined by the selected order of noise dependence when noise is sufficiently small. Our implementation guarantees positive estimates in finite samples.