Journal article
A frequency domain analysis of the error distribution from noisy high-frequency data
J Chang, A Delaigle, P Hall, CY Tang
Biometrika | OXFORD UNIV PRESS | Published : 2018
Abstract
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 ..
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Funding Acknowledgements
We are grateful to the editor, an associate editor and two referees for their helpful suggestions. Chang was supported in part by the Fundamental Research Funds for the Central Universities of China, the National Natural Science Foundation of China, and the Center of Statistical Research and the Joint Lab of Data Science and Business Intelligence at Southwestern University of Finance and Economics. Delaigle was supported by a Future Fellowship and a Discovery Project from the Australian Research Council. Hall was supported by a Laureate Fellowship and a Discovery Project from the Australian Research Council. Tang acknowledges support from the U.S. National Science Foundation.