We consider the problem of approximating sums of high-dimensional stationarytime series by Gaussian vectors, using the framework of functional dependencemeasure. The validity of the Gaussian approximation depends on the sample size$n$, the dimension $p$, the moment condition and the dependence of theunderlying processes. We also consider an estimator for long-run covariancematrices and study its convergence properties. Our results allow constructingsimultaneous confidence intervals for mean vectors of high-dimensional timeseries with asymptotically correct coverage probabilities. A Gaussianmultiplier bootstrap method is proposed. A simulation study indicates thequality of Gaussian approximation with different $n$, $p$ under differentmoment and dependence conditions.
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机译：我们使用函数相关性度量的框架来考虑用高斯向量近似高维平稳时间序列之和的问题。高斯近似的有效性取决于样本大小$ n $，维数$ p $，矩条件和基础过程的依赖性。我们还考虑了长期协方差矩阵的估计量，并研究了其收敛性。我们的结果允许构造渐近正确的覆盖概率的高维时间序列均值向量的同时置信区间。提出了一种高斯乘法器自举方法。仿真研究表明，在不同的矩和依赖条件下，具有不同的$ n $，$ p $的高斯近似的质量。
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