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

• 成果类型: Article
• 署名作者: Da, Rui; Xiu, Dacheng
• 署名单位: University of Chicago
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA15593
• 发表日期: 2021
• 页码: 2787-2825
• 关键词: maximum-likelihood-estimation; microstructure noise; INTEGRATED VOLATILITY; realized volatility; QUADRATIC VARIATION; long memory; selection; variance; jumps

摘要

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.