This paper proposes a new multilinear projection method for dimension-reduction in modeling high-dimensional matrix-variate time series. It assumes that a $p_1\times p_2$ matrix-variate time series consists of a dynamically dependent, lower-dimensional matrix-variate factor process and a $p_1\times p_2$ matrix white noise series. Covariance matrix of the vectorized white noises assumes a Kronecker structure such that the row and column covariances of the noise all have diverging/spiked eigenvalues to accommodate the case of low signal-to-noise ratio often encountered in applications, such as in finance and economics. We use an iterative projection procedure to {reduce the dimensions and noise effects in estimating} front and back loading matrices and {to} obtain faster convergence rates than those of the traditional methods available in the literature. Furthermore, we introduce a two-way projected Principal Component Analysis to mitigate the diverging noise effects, and implement a high-dimensional white-noise testing procedure to estimate the dimension of the factor matrix. Asymptotic properties of the proposed method are established as the dimensions and sample size go to infinity. Simulated and real examples are used to assess the performance of the proposed method. We also compared the proposed method with some existing ones in the literature concerning the forecasting ability of the identified factors and found that the proposed approach fares well in out-of-sample forecasting.

翻译：本文提出一种新的多线性投影方法，用于高维矩阵变时间序列建模中的降维。该方法假设一个$p_1\times p_2$的矩阵变时间序列由动态相关的低维矩阵变因子过程和$p_1\times p_2$的矩阵白噪声序列构成。向量化白噪声的协方差矩阵具有Kronecker结构，其行列噪声协方差均呈发散/尖峰特征值分布，以应对金融、经济等应用中常见的低信噪比情形。我们采用迭代投影程序来{降低维度和噪声影响}以估计前后载荷矩阵，{并}获得比文献中传统方法更快的收敛速度。此外，引入双向投影主成分分析法以缓解发散噪声效应，并通过高维白噪声检验程序估计因子矩阵维度。当维度和样本量趋于无穷时，所提方法的渐近性质得以建立。通过模拟和实际案例评估方法性能，同时将本方法与传统方法在因子预测能力方面进行比较，结果表明本方法在样本外预测中表现良好。