High-dimensional volatility matrix estimation via wavelets and thresholding

• 成果类型: Article
• 署名作者: Fryzlewicz, P.
• 署名单位: University of London; London School Economics & Political Science
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/ast033
• 发表日期: 2013
• 页码: 921938
• 关键词: covariance; nonstationarities; distributions; coherence

摘要

We propose a locally stationary linear model for the evolution of high-dimensional financial returns, where the time-varying volatility matrix is modelled as a piecewise-constant function of time. We introduce a new wavelet-based technique for estimating the volatility matrix, which combines four ingredients: a Haar wavelet decomposition, variance stabilization of the Haar coefficients via the Fisz transform prior to thresholding, a bias correction, and extra time-domain thresholding, soft or hard. Under the assumption of sparsity, we demonstrate the interval-wise consistency of the proposed estimators of the volatility matrix and its inverse in the operator norm, with rates that adapt to the features of the target matrix. We also propose a version of the estimators based on the polarization identity, which permits a more precise derivation of the thresholds. We discuss the practicalities of the algorithm, including parameter selection and how to perform it online. A simulation study shows the benefits of the method, which is illustrated using a stock index portfolio.