Econometrica Vol. 89 No. 6 2021
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 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.
- DOI
- 10.3982/ecta15593
- Volume
- 89
- Issue
- 6
- Pages
- 2787-2825
- Language
- en
- Sources
- bibtex:phds-export.bib openalex crossref