A frequency domain analysis of the error distribution from noisy high-frequency data

• 成果类型: Article
• 署名作者: Chang, Jinyuan; Delaigle, Aurore; Hall, Peter; Tang, Chengyong
• 署名单位: Southwestern University of Finance & Economics - China; University of Melbourne; Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asy006
• 发表日期: 2018
• 页码: 353369
• 关键词: market-microstructure noise; functional data-analysis; Nonparametric Regression; INTEGRATED VOLATILITY; DENSITY-ESTIMATION; Matrix Estimation; ito processes; deconvolution; CONVERGENCE; variance

摘要

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 Ito 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.