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CP-factorization for high dimensional tensor time series and double projection iterations

Jinyuan Chang, Guanglin Huang, Qiwei Yao, Long Yu

arXiv 7 Jun 2026 · Statistics — Methodology

arXiv:2606.08560 · PDF · DOI · OpenAlex · Extracted main text

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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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Chang, J., He, J., Yang, L., and Yao, Q (2023) Modelling matrix time series via a tensor CP-decomposition self1.000225100%
2Han, Y., Yang, D., Zhang, C.-H., and Chen, R (2024) CP factor model for dynamic tensors1.000215100%
3Chen, B., Han, Y., and Yu, Q (2026) Estimation and inference for CP tensor factor models1.00053100%
4Chang, J., Guo, B., and Yao, Q (2015) High dimensional stochastic regression with latent factors, endogeneity and nonlinearity self0.64422100%
5Kolda, T. G. and Bader, B. W (2009) Tensor decompositions and applications0.64422100%
6Lam, C. and Yao, Q (2012) Factor modeling for high-dimensional time series: inference for the number of factors self0.64422100%
7Chang, J., Du, Y., Huang, G., and Yao, Q (2026) Identification and estimation for matrix time series CP-factor models self0.58531100%
8He, Y., Hou, Y., Wang, Y., and Zhou, W.-X (2026) Estimation of tensor factor model by iterative least squares0.40511100%
9Liu, Z., Hu, B., Wang, L., Wu, F., Gao, W., and Wang, Y (2015) Seasonal and diurnal variation in particulate matter (PM10 and PM2.5) at an urban site of Beijing: analyses from a 9-year study0.40511100%
10Andrews, D. W (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation0.40511100%

Showing the top 10 of 54 scored citations.