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

Rui Da and Dacheng Xiu

Econometrica, 2021, vol. 89, issue 6, 2787-2825

Abstract: 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 n1/4 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.

Date: 2021
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