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.

翻译：本文采用规范多元分解（CP分解）对高维张量时间序列进行建模。核心目标是识别并估计CP分解中的因子载荷矩阵。我们提出一种基于数据序列依赖结构构建矩阵的标准特征分析的单一流程估计方法。在因子载荷向量线性无关的一般条件下，该方法可容许因子存在相关性且载荷向量非近似正交，并建立了估计量的渐近性质。该程序能自适应处理因子载荷向量的稀疏性，兼容弱因子场景，在多种情境下展现出优异性能。为进一步降低估计误差，我们引入基于新型双投影方法的迭代算法。理论证明了迭代估计量的收敛速率提升特性，并推导出相应的极限分布。同时给出渐近方差的一致估计量，这对相关推断问题具有关键作用。所有结论均通过大量仿真实验及两项真实数据应用得到验证。