A frequency domain analysis of the error distribution from noisy high-frequency data. (6th March 2018)

• Record Type: Journal Article
• Authors: Chang, Jinyuan; Delaigle, Aurore; Hall, Peter; Tang, Cheng Yong
• Is Part Of: Biometrika. Volume 105:Number 2(2018:Jun.)
• Page Start: 353
• Page End: 369
• Publication Date: 2018-03-06
• Subjects: Deconvolution -- Fourier transform -- Functional data -- High-frequency data -- Measurement error -- Smoothing; Biometry -- Periodicals; 570.1519505
• DOI: 10.1093/biomet/asy006
• Languages: English
• ISSNs: 0006-3444

Abstract

SUMMARY: Data observed at a high sampling frequency are typically assumed to be an additive composite of a relatively slow-varying continuous-time component, a latent stochastic process or smooth random function, and measurement error. Supposing that the latent component is an Itô diffusion process, we propose to estimate the measurement error density function by applying a deconvolution technique with appropriate localization. Our estimator, which does not require equally-spaced observed times, is consistent and minimax rate-optimal. We also investigate estimators of the moments of the error distribution and their properties, propose a frequency domain estimator for the integrated volatility of the underlying stochastic process, and show that it achieves the optimal convergence rate. Simulations and an application to real data validate our analysis.