When Moving‐Average Models Meet High‐Frequency Data: Uniform Inference on Volatility. Issue 6 (11th November 2021)

• Record Type: Journal Article
• Authors: Da, Rui; Xiu, Dacheng
• Is Part Of: Econometrica. Volume 89:Issue 6(2021)
• Page Start: 2787
• Page End: 2825
• Publication Date: 2021-11-11
• Subjects: QMLE -- serially correlated noise -- small noise -- model selection -- uniformity; Econometrics -- Periodicals; Economics, Mathematical -- Periodicals; Economics -- Periodicals; Économétrie -- Périodiques; Mathématiques économiques -- Périodiques; Économie politique -- Périodiques; 330.05
• DOI: 10.3982/ECTA15593
• Languages: English
• ISSNs: 0012-9682

Abstract

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.