In this paper, we consider diffusion index forecasting with both tensor and non-tensor predictors, where the tensor structure is preserved with a Canonical Polyadic (CP) tensor factor model. When the number of non-tensor predictors is small, we study the asymptotic properties of the least squares estimator in this tensor factor-augmented regression, allowing for factors with different strengths. We derive an analytical formula for prediction intervals that accounts for the estimation uncertainty of the latent factors. In addition, we propose a novel thresholding estimator for the high-dimensional covariance matrix that is robust to cross-sectional dependence. When the number of non-tensor predictors exceeds or diverges with the sample size, we introduce a multi-source factor-augmented sparse regression model and establish the consistency of the corresponding penalized estimator. Simulation studies validate our theoretical results and an empirical application to U.S. trade flows demonstrates the advantages of our approach over other popular methods in the literature.

翻译：本文研究同时包含张量与非张量预测变量的扩散指数预测问题，其中张量结构通过规范多元（CP）张量因子模型进行保持。当非张量预测变量数量较少时，我们研究了该张量因子增强回归中最小二乘估计量的渐近性质，允许因子具有不同强度。我们推导了考虑潜因子估计不确定性的预测区间解析公式。此外，我们提出了一种对横截面依赖具有鲁棒性的高维协方差矩阵阈值估计器。当非张量预测变量数量超过样本量或随样本量发散时，我们引入多源因子增强稀疏回归模型，并建立了相应惩罚估计量的一致性。模拟研究验证了我们的理论结果，对美国贸易流的实证应用展示了本方法相较于文献中其他主流方法的优势。