GAUSSIAN APPROXIMATION FOR HIGH DIMENSIONAL TIME SERIES

• 成果类型: Article
• 署名作者: Zhang, Danna; Wu, Wei Biao
• 署名单位: University of California System; University of California San Diego; University of Chicago
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/16-AOS1512
• 发表日期: 2017
• 页码: 1895-1919
• 关键词: sample correlation-matrices; central-limit-theorem; nonparametric-estimation; asymptotic-distribution; COVARIANCE-MATRIX; largest entries; deviations; estimator; sums

摘要

We consider the problem of approximating sums of high dimensional stationary time series by Gaussian vectors, using the framework of functional dependence measure. The validity of the Gaussian approximation depends on the sample size n, the dimension p, the moment condition and the dependence of the underlying processes. We also consider an estimator for long-run covariance matrices and study its convergence properties. Our results allow constructing simultaneous confidence intervals for mean vectors of high-dimensional time series with asymptotically correct coverage probabilities. As an application, we propose a Kolmogorov-Smirnov-type statistic for testing distributions of high-dimensional time series.