Constrained Factor Models for High-Dimensional Matrix-Variate Time Series

By Elynn Y. Chen, Ruey S. Tsay, Rong Chen. Journal of the American Statistical Association, 2017

119 citations recorded by the source corpus.

Abstract High-dimensional matrix-variate time series data are becoming widely available in many scientific fields, such as economics, biology, and meteorology. To achieve significant dimension reduction while preserving the intrinsic matrix structure and temporal dynamics in such data, Wang, Liu, and Chen proposed a matrix factor model, that is, shown to be able to provide effective analysis. In this article, we establish a general framework for incorporating domain and prior knowledge in the matrix factor model through linear constraints. The proposed framework is shown to be useful in achieving parsimonious parameterization, facilitating interpretation of the latent matrix factor, and identifying specific factors of interest. Fully utilizing the prior-knowledge-induced constraints results in more efficient and accurate modeling, inference, dimension reduction as well as a clear and better interpretation of the results. Constrained, multi-term, and partially constrained factor models for matrix-variate time series are developed, with efficient estimation procedures and their asymptotic properties. We show that the convergence rates of the constrained factor loading matrices are much faster than those of the conventional matrix factor analysis under many situations. Simulation studies are carried out to demonstrate finite-sample performance of the proposed method and its associated asymptotic properties. We illustrate the proposed model with three applications, where the constrained matrix-factor models outperform their unconstrained counterparts in the power of variance explanation under the out-of-sample 10-fold cross-validation setting. Supplementary materials for this article are available online.

Subfields: Applied Mathematics, Computational Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a57113aa655b4d3c519a046cd749ce1fbe6df133

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Citations in the corpus

Statistical Inference for High-Dimensional Matrix-Variate Factor Models (2020, methodology): “With respect to statistical analyses, Wang et al. (2019) and Chen et al. (2019) consider a similar model in the bilinear form (1.1), yet under a very di ﬀ erent setting where E t is assumed to be white noise (Lam and Yao, 2012; Lam et al., 2011).”
Modelling matrix time series via a tensor CP-decomposition (2021, methodology): “• (MAR) Fit {Yt}(336) t=1 by the matrix-AR(1) of Chen et al. (2021), which involves 200 parameters.”