When Moving-Average Models Meet High-Frequency Data: Uniform Inference on Volatility
Econometrica · 2021 · Volume 89 · Issue 6
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 dominatesn1/4as 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, serially correlated noise, small noise, model selection, uniformity
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