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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.26297 |
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Table of Contents:
- This article explores a general factor structure for high-dimensional nonstationary functional time series, encompassing a wide range of factor models studied in the existing literature. We investigate the asymptotic spectral behaviors of the sample covariance operator under this general data structure. A novel fundamental sufficient condition, formulated in terms of a newly introduced effective rank tailored to this setup, is established under which empirical eigen-analysis yields spurious results, rendering sample eigenvalues and eigenvectors unreliable for accurately recovering the underlying factor structure. This generalizes the results of Onatski and Wang [2021] from typical high-dimensional time series (HDTS) to the more intricate functional framework. The newly defined effective rank is rigorously analyzed through a decomposition of the effects attributable to functional factor loadings and functional factors. Contrary to the findings in the HDTS setting, empirical eigen-analysis of models with only a small number of strong non-stationary factors may still produce spurious limits in the functional framework. Therefore, additional caution is warranted when applying covariance-based statistical methods to potentially nonstationary functional data. Simulation studies are performed to determine conditions under which spurious limits occur. Real data analysis on age-specific mortality rate data from multiple locations is conducted for evidence of spurious factors induced by empirical eigen-analysis.