CP-factorization for high dimensional tensor time series and double projection iterations
Abstract
We adopt the canonical polyadic (CP) decomposition to model high-dimensional tensor time series. Our primary goal is to identify and estimate the factor loadings in the CP decomposition. We propose a one-pass estimation procedure through standard eigen-analysis for a matrix constructed based on the serial dependence structure of the data. The asymptotic properties of the proposed estimator are established under a general setting as long as the factor loading vectors are linearly independent, allowing the factors to be correlated and the factor loading vectors to be not nearly orthogonal. The procedure adapts to the sparsity of the factor loading vectors, accommodates weak factors, and demonstrates strong performance across a wide range of scenarios. To further reduce estimation errors, we also introduce an iterative algorithm based on a novel double projection approach. We theoretically justify the improved convergence rate of the iterative estimator, and derive the associated limiting distribution. A consistent estimator of the asymptotic variance is also provided, which plays a key role in the related inference problems. All results are validated through extensive simulations and two real data applications.
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BibTeX
@misc{chang2026cpfactorization,
title = {{CP-factorization for high dimensional tensor time series and double projection iterations}},
author = {Jinyuan Chang and Guanglin Huang and Qiwei Yao and Long Yu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.08560},
eprint = {2606.08560},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.08560},
}
RIS
TY - UNPB
TI - CP-factorization for high dimensional tensor time series and double projection iterations
AU - Jinyuan Chang
AU - Guanglin Huang
AU - Qiwei Yao
AU - Long Yu
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2606.08560
UR - https://arxiv.org/abs/2606.08560
AB - We adopt the canonical polyadic (CP) decomposition to model high-dimensional tensor time series. Our primary goal is to identify and estimate the factor loadings in the CP decomposition. We propose a one-pass estimation procedure through standard eigen-analysis for a matrix constructed based on the serial dependence structure of the data. The asymptotic properties of the proposed estimator are established under a general setting as long as the factor loading vectors are linearly independent, allowing the factors to be correlated and the factor loading vectors to be not nearly orthogonal. The procedure adapts to the sparsity of the factor loading vectors, accommodates weak factors, and demonstrates strong performance across a wide range of scenarios. To further reduce estimation errors, we also introduce an iterative algorithm based on a novel double projection approach. We theoretically justify the improved convergence rate of the iterative estimator, and derive the associated limiting distribution. A consistent estimator of the asymptotic variance is also provided, which plays a key role in the related inference problems. All results are validated through extensive simulations and two real data applications.
ER -