LOCAL WHITTLE ESTIMATION OF HIGH-DIMENSIONAL LONG-RUN VARIANCE AND PRECISION MATRICES

• 成果类型: Article
• 署名作者: Baek, Changryong; Duker, Marie-christine; Pipiras, Vladas
• 署名单位: Sungkyunkwan University (SKKU); Cornell University; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/23-AOS2330
• 发表日期: 2023
• 页码: 2386-2414
• 关键词: gaussian semiparametric estimation; large covariance; regularized estimation; PENALIZED LIKELIHOOD; model selection; SPARSE; shrinkage; Lasso

摘要

This work develops nonasymptotic theory for estimation of the longrun variance matrix and its inverse, the so-called precision matrix, for highdimensional time series under general assumptions on the dependence structure including long-range dependence. The estimation involves shrinkage techniques, which are thresholding and penalizing versions of the classical multivariate local Whittle estimator. The results ensure consistent estimation in a double asymptotic regime where the number of component time series is allowed to grow with the sample size as long as the true model parameters are sparse. The key technical result is a concentration inequality of the local Whittle estimator for the long-run variance matrix around the true model parameters. In particular, it handles simultaneously the estimation of the memory parameters, which enter the underlying model. Novel algorithms for the considered procedures are proposed, and a simulation study and a data application are also provided.