Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/319337 
Year of Publication: 
2024
Citation: 
[Journal:] Journal of Time Series Analysis [ISSN:] 1467-9892 [Volume:] 46 [Issue:] 3 [Publisher:] John Wiley & Sons, Ltd [Place:] Oxford, UK [Year:] 2024 [Pages:] 402-420
Publisher: 
John Wiley & Sons, Ltd, Oxford, UK
Abstract: 
Analyzing the covariance structure of data is a fundamental task of statistics. While this task is simple for low‐dimensional observations, it becomes challenging for more intricate objects, such as multi‐variate functions. Here, the covariance can be so complex that just saving a non‐parametric estimate is impractical and structural assumptions are necessary to tame the model. One popular assumption for space‐time data is separability of the covariance into purely spatial and temporal factors. In this article, we present a new test for separability in the context of dependent functional time series. While most of the related work studies functional data in a Hilbert space of square integrable functions, we model the observations as objects in the space of continuous functions equipped with the supremum norm. We argue that this (mathematically challenging) setup enhances interpretability for users and is more in line with practical preprocessing. Our test statistic measures the maximal deviation between the estimated covariance kernel and a separable approximation. Critical values are obtained by a non‐standard multiplier bootstrap for dependent data. We prove the statistical validity of our approach and demonstrate its practicability in a simulation study and a data example.
Subjects: 
Dependent multiplier bootstrap
space‐time data
separability
Banach space
functional time series
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by-nc-nd Logo
Document Type: 
Article
Document Version: 
Published Version
Appears in Collections:

Files in This Item:
File
Size





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.