EFFICIENT ESTIMATION OF INTEGRATED VOLATILITY FUNCTIONALS UNDER GENERAL VOLATILITY DYNAMICS. (17th August 2021)

• Record Type: Journal Article
• Authors: Li, Jia; Liu, Yunxiao
• Is Part Of: Econometric theory. Volume 37:Number 4(2021)
• Page Start: 664
• Page End: 707
• Publication Date: 2021-08-17
• Subjects: Econometrics -- Periodicals; 330.01519505
• DOI: 10.1017/S0266466620000274
• Languages: English
• ISSNs: 0266-4666

Abstract

Abstract : We provide an asymptotic theory for the estimation of a general class of smooth nonlinear integrated volatility functionals. Such functionals are broadly useful for measuring financial risk and estimating economic models using high-frequency transaction data. The theory is valid under general volatility dynamics, which accommodates both Itô semimartingales (e.g., jump-diffusions) and long-memory processes (e.g., fractional Brownian motions). We establish the semiparametric efficiency bound under a nonstandard nonergodic setting with infill asymptotics, and show that the proposed estimator attains this efficiency bound. These results on efficient estimation are further extended to a setting with irregularly sampled data.