提出一种更稳定高效的矩阵时间序列因子模型估计方法。
Identification and estimation for matrix time series CP-factor models
- 通过联合对角化多个矩阵实现因子识别，避免特征值间隙影响。
- 在模拟与真实数据上均表现更优，尤其适用于低秩因子载荷矩阵。
- 适合处理传统方法失效的复杂高维矩阵时间序列数据。
我们提出一种新的矩阵时间序列CP因子模型的识别与估计方法。与基于广义特征分析的方法（Chang等, 2023）不同，该方法不依赖于矩阵扰动理论，因此其估计量的收敛速度不受小特征值间隙的影响。该方法将问题转化为若干矩阵的联合对角化，这些矩阵的元素由线性系统的基确定，并通过精心选择基来避免近共线性问题（见命题5及第4.3节）。此外，不同于Chang等（2023）要求两个因子载荷矩阵满秩，本方法可处理秩亏的因子载荷矩阵。通过模拟和真实矩阵时间序列数据的实验，验证了该方法的优势。
原文摘要 · Abstract (English)
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 of the associated estimators 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). Furthermore, unlike Chang et al. (2023) which requires the two factor loading matrices to be full-ranked, the proposed 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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。