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This paper proposes a new multilinear projection method fordimension-reduction in modeling high-dimensional matrix-variate time series. Itassumes that a $p_1\times p_2$ matrix-variate time series consists of adynamically dependent, lower-dimensional matrix-variate factor process and a$p_1\times p_2$ matrix white noise series. Covariance matrix of the vectorizedwhite noises assumes a Kronecker structure such that the row and columncovariances of the noise all have diverging/spiked eigenvalues to accommodatethe case of low signal-to-noise ratio often encountered in applications, suchas in finance and economics. We use an iterative projection procedure to{reduce the dimensions and noise effects in estimating} front and back loadingmatrices and {to} obtain faster convergence rates than those of the traditionalmethods available in the literature. Furthermore, we introduce a two-wayprojected Principal Component Analysis to mitigate the diverging noise effects,and implement a high-dimensional white-noise testing procedure to estimate thedimension of the factor matrix. Asymptotic properties of the proposed methodare established as the dimensions and sample size go to infinity. Simulated andreal examples are used to assess the performance of the proposed method. Wealso compared the proposed method with some existing ones in the literatureconcerning the forecasting ability of the identified factors and found that theproposed approach fares well in out-of-sample forecasting.

Denoising and Multilinear Dimension-Reduction of High-Dimensional Matrix-Variate Time Series via a Factor Model