When Moving‐Average Models Meet High‐Frequency Data: Uniform Inference on Volatility

We propose uniformly valid inference on volatility with noisy high-frequency data. We assume the observed transaction price follows a continuous-time Ito-semimartingale, contaminated by a discrete-time moving-average noise process associated with the arrival of trades. We estimate the quadratic variation of the semimartingale by maximizing the likelihood of a misspecified moving-average model, with its order selected based on the information criteria. Our inference is uniformly valid over a large class of noise processes whose magnitude and dependence structure vary with sample size. Our implementation is tuning free barring order selection, and it yields positive estimates in finite samples. Finally, we provide consistent estimators of noise autocovariances as byproducts, which also play a critical role in achieving uniformity.