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We derive and study a significance test for determining if a panel of functional time series is separable. In the context of this paper, separability means that the covariance structure factors into the product of two functions, one depending only on time and the other depending only on the coordinates of the panel. Separability is a property which can dramatically improve computational efficiency by substantially reducing model complexity. It is especially useful for functional data as it implies that the functional principal components are the same for each member of the panel. However such an assumption must be verified before proceeding with further inference. Our approach is based on functional norm differences and provides a test with well controlled size and high power. We establish our procedure quite generally, allowing one to test separability of autocovariances as well. In addition to an asymptotic justification, our methodology is validated by a simulation study. It is applied to functional panels of particulate pollution and stock market data.
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Monitoring panels of sparse functional data
Panels of random functions are common in applications of functional data analysis. They often occur when sequences of functions are observed at a number of different locations. We propose a methodology to monitor for structural breaks in such panels and to identify the changing components with statistical certainty. Our approach relies on a Full‐CUSUM statistic that has proved to be powerful in finite dimensions but has not been applied to functional data. To account for the practically relevant problem of sparsity, we formulate our results for triangular arrays of nonstationary, sparse estimators. The derivation of our asymptotic theory relies on new Gaussian approximations on the Banach space of continuous functions, which imply new convergence results for the change point detectors. We illustrate our approach with a simulation study and application to intraday returns on exchange traded funds.
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- Award ID(s):
- 2412408
- PAR ID:
- 10677008
- Publisher / Repository:
- wileyonlinelibrary.com
- Date Published:
- Journal Name:
- Journal of Time Series Analysis
- Volume:
- 47
- Issue:
- 3
- ISSN:
- 0143-9782
- Page Range / eLocation ID:
- 660 to 674
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1111/jtsa.12796
