Econometrica: Nov, 2021, Volume 89, Issue 6

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

https://doi.org/10.3982/ECTA15593
p. 2787-2825

Rui Da, Dacheng Xiu

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.

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