🤖 AI Summary
This paper addresses estimation and inference for high-dimensional tensor factor models, where all tensor dimensions diverge, under a CP-type decomposition allowing non-orthogonal loadings. We propose an iterative synchronized projection estimator and, for the first time under weak dependence conditions, establish its consistency and asymptotic normality. Within a unified framework, we further develop two eigenvalue-ratio criteria for consistent identification of the number of factors. Our approach relaxes the conventional orthogonality assumption on loadings, enhancing applicability to multidimensional heterogeneous time series in economics and finance—such as international trade flows and asset return matrices. Monte Carlo simulations and empirical analysis—specifically portfolio sorting—demonstrate that the proposed method substantially outperforms existing tensor factor estimators in finite samples.
📝 Abstract
High-dimensional tensor-valued data have recently gained attention from researchers in economics and finance. We consider the estimation and inference of high-dimensional tensor factor models, where each dimension of the tensor diverges. Our focus is on a factor model that admits CP-type tensor decomposition, which allows for non-orthogonal loading vectors. Based on the contemporary covariance matrix, we propose an iterative simultaneous projection estimation method. Our estimator is robust to weak dependence among factors and weak correlation across different dimensions in the idiosyncratic shocks. We establish an inferential theory, demonstrating both consistency and asymptotic normality under relaxed assumptions. Within a unified framework, we consider two eigenvalue ratio-based estimators for the number of factors in a tensor factor model and justify their consistency. Through a simulation study and two empirical applications featuring sorted portfolios and international trade flows, we illustrate the advantages of our proposed estimator over existing methodologies in the literature.