This paper proposes a new AR-sieve bootstrap approach on high-dimensional time series. The major challenge of classical bootstrap methods on high-dimensional time series is two-fold: the curse dimensionality and temporal dependence. To tackle such difficulty, we utilise factor modelling to reduce dimension and capture temporal dependence simultaneously. A factor-based bootstrap procedure is constructed, which conducts AR-sieve bootstrap on the extracted low-dimensional common factor time series and then recovers the bootstrap samples for original data from the factor model. Asymptotic properties for bootstrap mean statistics and extreme eigenvalues are established. Various simulations further demonstrate the advantages of the new AR-sieve bootstrap under high-dimensional scenarios. Finally, an empirical application on particulate matter (PM) concentration data is studied, where bootstrap confidence intervals for mean vectors and autocovariance matrices are provided.

翻译：本文建议对高维时间序列采用新的AR-Sieve 靴子捕捉装置。 古典靴子捕捉方法在高维时间序列上的主要挑战有两个方面: 诅咒维度和时间依赖性。 为了应对这种困难,我们同时使用要素模型来减少尺寸和捕捉时间依赖性。 正在建立一个基于要素的靴子捕捉程序,在提取的低维共同系数时间序列上进行AR-Sieve 靴子捕捉装置,然后从元素模型中提取原始数据的靴子捕捉样品。 建立了靴子捕捉平均统计数据和极端电子价值的吸附特性。 各种模拟进一步展示了在高维情景下新的AR- sieve 靴子陷阱的优势。 最后,正在研究对颗粒物质浓度数据的经验应用,其中提供了平均矢量和自动变异矩阵的靴子捕捉信任间隔。