We propose a new method for identifying and estimating the CP-factor models for matrix time series. Unlike the generalized eigenanalysis-based method of Chang et al.(2023) for which the convergence rates may suffer from small eigengaps as the asymptotic theory is based on some matrix perturbation analysis, the proposed new method enjoys faster convergence rates which are free from any eigengaps. It achieves this by turning the problem into a joint diagonalization of several matrices whose elements are determined by a basis of a linear system, and by choosing the basis carefully to avoid near co-linearity (see Proposition 5 and Section 4.3 below). Furthermore, unlike Chang et al.(2023) which requires the two factor loading matrices to be full-ranked, the new method can handle rank-deficient factor loading matrices. Illustration with both simulated and real matrix time series data shows the advantages of the proposed new method.

翻译：本文提出了一种用于识别和估计矩阵时间序列CP因子模型的新方法。与Chang等人（2023）基于广义特征分析的现有方法相比——该方法由于渐近理论建立在矩阵扰动分析基础上，其收敛速度可能受小特征值间隙影响——本文提出的新方法具有更快的收敛速度，且完全不受任何特征值间隙限制。这一优势的取得，是通过将问题转化为对多个矩阵的联合对角化来实现的，这些矩阵的元素由线性系统的一组基决定；同时通过精心选择基以避免近似共线性（详见下文命题5与第4.3节）。此外，与Chang等人（2023）要求两个因子载荷矩阵必须满秩不同，新方法能够处理秩亏缺的因子载荷矩阵。通过模拟与真实矩阵时间序列数据的实证分析，验证了所提新方法的优越性。