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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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Core shrinkage covariance estimation for matrix-variate data
Abstract A separable covariance model can describe the among-row and among-column correlations of a random matrix and permits likelihood-based inference with a very small sample size. However, if the assumption of separability is not met, data analysis with a separable model may misrepresent important dependence patterns in the data. As a compromise between separable and unstructured covariance estimation, we decompose a covariance matrix into a separable component and a complementary ‘core’ covariance matrix. This decomposition defines a new covariance matrix decomposition that makes use of the parsimony and interpretability of a separable covariance model, yet fully describes covariance matrices that are non-separable. This decomposition motivates a new type of shrinkage estimator, obtained by appropriately shrinking the core of the sample covariance matrix, that adapts to the degree of separability of the population covariance matrix.
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- Award ID(s):
- 2203741
- PAR ID:
- 10501824
- Publisher / Repository:
- Royal Statistical Society
- Date Published:
- Journal Name:
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Volume:
- 85
- Issue:
- 5
- ISSN:
- 1369-7412
- Page Range / eLocation ID:
- 1659 to 1679
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/jrsssb/qkad070
