TESTING FOR PERIODICITY IN FUNCTIONAL TIME SERIES

• 成果类型: Article
• 署名作者: Hoermann, Siegfried; Kokoszka, Piotr; Nisol, Gilles
• 署名单位: Graz University of Technology; Colorado State University System; Colorado State University Fort Collins; Universite Libre de Bruxelles
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/17-AOS1645
• 发表日期: 2018
• 页码: 2960-2984
• 关键词: model; components

摘要

We derive several tests for the presence of a periodic component in a time series of functions. We consider both the traditional setting in which the periodic functional signal is contaminated by functional white noise, and a more general setting of a weakly dependent contaminating process. Several forms of the periodic component are considered. Our tests are motivated by the likelihood principle and fall into two broad categories, which we term multivariate and fully functional. Generally, for the functional series that motivate this research, the fully functional tests exhibit a superior balance of size and power. Asymptotic null distributions of all tests are derived and their consistency is established. Their finite sample performance is examined and compared by numerical studies and application to pollution data.