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High-dimensional low-rank tensor autoregressive time series modeling

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  • Wang, Di
  • Zheng, Yao
  • Li, Guodong

Abstract

Modern technological advances have enabled an unprecedented amount of structured data with complex temporal dependence, urging the need for new methods to efficiently model and forecast high-dimensional tensor-valued time series. This paper provides a new modeling framework to accomplish this task via autoregression (AR). By considering a low-rank Tucker decomposition for the transition tensor, the proposed tensor AR can flexibly capture the underlying low-dimensional tensor dynamics, providing both substantial dimension reduction and meaningful multi-dimensional dynamic factor interpretations. For this model, we first study several nuclear-norm-regularized estimation methods and derive their non-asymptotic properties under the approximate low-rank setting. In particular, by leveraging the special balanced structure of the transition tensor, a novel convex regularization approach based on the sum of nuclear norms of square matricizations is proposed to efficiently encourage low-rankness of the coefficient tensor. To further improve the estimation efficiency under exact low-rankness, a non-convex estimator is proposed with a gradient descent algorithm, and its computational and statistical convergence guarantees are established. Simulation studies and an empirical analysis of tensor-valued time series data from multi-category import-export networks demonstrate the advantages of the proposed approach.

Suggested Citation

  • Wang, Di & Zheng, Yao & Li, Guodong, 2024. "High-dimensional low-rank tensor autoregressive time series modeling," Journal of Econometrics, Elsevier, vol. 238(1).
  • Handle: RePEc:eee:econom:v:238:y:2024:i:1:s0304407623002609
    DOI: 10.1016/j.jeconom.2023.105544
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    3. Yugang He, 2024. "E-commerce and foreign direct investment: pioneering a new era of trade strategies," Palgrave Communications, Palgrave Macmillan, vol. 11(1), pages 1-14, December.

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