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

Abstract

We conduct 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 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.

Keywords: QMLE, Dependent Noise, Small Noise, Model Selection, Uniformity

JEL Classification: C13, C14, C55, C58