The Maximum of the Periodogram of a Sequence of Functional Data

• 成果类型: Article
• 署名作者: Cerovecki, Clement; Characiejus, Vaidotas; Hoermann, Siegfried
• 署名单位: KU Leuven; Universite Libre de Bruxelles; University of Southern Denmark; Graz University of Technology
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2071720
• 发表日期: 2023
• 页码: 2712-2720
• 关键词: approximate bayesian computation; inference; likelihood; population; EFFICIENCY

摘要

We study the periodogram operator of a sequence of functional data. Using recent advances in Gaussian approximation theory, we derive the asymptotic distribution of the maximum norm over all fundamental frequencies. We consider the case where the noise variables are independent and then generalize our results to functional linear processes. Our theory can be used for detecting periodic signals in functional time series when the length of the period is unknown. We demonstrate the proposed methodology in a simulation study as well as on real data. Supplementary materials for this article are available online.