Statistical inference for high-dimensional panel functional time series

• 成果类型: Article
• 署名作者: Zhou, Zhou; Dette, Holger
• 署名单位: University of Toronto; Ruhr University Bochum; University of Toronto
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkad015
• 发表日期: 2023
• 页码: 523-549
• 关键词: Gaussian Approximation; Uniform Inference; data models; regression; TRENDS; POWER

摘要

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.