🤖 AI Summary
This paper addresses diffusion index forecasting with both tensor and non-tensor predictors, proposing a factor-augmented regression framework that preserves the intrinsic tensor structure. Methodologically: (1) it constructs a latent factor model via CP decomposition to explicitly capture the multilinear structure of high-dimensional tensor data; (2) it derives asymptotically efficient prediction intervals accounting for estimation uncertainty in latent factors; and (3) it designs a cross-sectionally robust thresholded covariance estimator, integrated with multi-source sparse penalized regression to tackle high-dimensional variable selection under small-sample settings. Theoretical analysis establishes consistency and robustness, corroborated by extensive simulations. In an empirical application to U.S. trade flow data, the method significantly outperforms conventional factor models and LASSO-based approaches, delivering superior forecasting accuracy and statistical reliability for structured heterogeneous data.
📝 Abstract
In this paper, we consider diffusion index forecast 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-squared 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 US trade flows demonstrates the advantages of our approach over other popular methods in the literature.