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August 2021 Volatility coupling
Jean Jacod, Jia Li, Zhipeng Liao
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Ann. Statist. 49(4): 1982-1998 (August 2021). DOI: 10.1214/20-AOS2023

Abstract

This paper provides a strong approximation, or coupling, theory for spot volatility estimators formed using high-frequency data. We show that the t-statistic process associated with the nonparametric spot volatility estimator can be strongly approximated by a growing-dimensional vector of independent variables defined as functions of Brownian increments. We use this coupling theory to study the uniform inference for the volatility process in an infill asymptotic setting. Specifically, we propose uniform confidence bands for spot volatility, beta, idiosyncratic variance processes, and their nonlinear transforms. The theory is also applied to address an open question concerning the inference of monotone nonsmooth integrated volatility functionals such as the occupation time and its quantiles.

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Jean Jacod. Jia Li. Zhipeng Liao. "Volatility coupling." Ann. Statist. 49 (4) 1982 - 1998, August 2021. https://doi.org/10.1214/20-AOS2023

Information

Received: 1 March 2020; Revised: 1 July 2020; Published: August 2021
First available in Project Euclid: 29 September 2021

Digital Object Identifier: 10.1214/20-AOS2023

Subjects:
Primary: 60F15 , 60G44 , 62G20

Keywords: coupling , high-frequency data , occupation measure , quantiles , Semimartingale , uniform inference

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 4 • August 2021
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