Statistical inference for high-dimensional panel functional time series
针对高维面板函数型时间序列，提出物理依赖过程的新概念，推导高斯和乘子自助法逼近，用于构建均值函数的联合置信带和检验面板均值函数是否平行。
Abstract In this paper, we develop statistical inference tools for high-dimensional functional time series. We introduce a new concept of physical dependent processes in the space of square integrable functions, which adopts the idea of basis decomposition of functional data in these spaces, and derive Gaussian and multiplier bootstrap approximations for sums of high-dimensional functional time series. These results have numerous important statistical consequences. Exemplarily, we consider the development of joint simultaneous confidence bands for the mean functions and the construction of tests for the hypotheses that the mean functions in the panel dimension are parallel. The results are illustrated by means of a small simulation study and in the analysis of Canadian temperature data.