Testing for periodicity in functional time series

Siegfried Hörmann, Piotr Kokoszka, Gilles Nisol

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)2960-2984
Number of pages26
JournalThe Annals of Statistics
Issue number6A
Publication statusPublished - 2018


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