Modelling matrix time series via a tensor CP-decomposition
提出一种基于广义特征分析的非迭代方法，通过张量CP分解对矩阵时间序列建模，能有效降维并提升预测性能，适用于金融、经济等领域的矩阵数据。
Abstract We consider to model matrix time series based on a tensor canonical polyadic (CP)-decomposition. Instead of using an iterative algorithm which is the standard practice for estimating CP-decompositions, we propose a new and one-pass estimation procedure based on a generalized eigenanalysis constructed from the serial dependence structure of the underlying process. To overcome the intricacy of solving a rank-reduced generalized eigenequation, we propose a further refined approach which projects it into a lower-dimensional full-ranked eigenequation. This refined method can significantly improve the finite-sample performance. We show that all the component coefficient vectors in the CP-decomposition can be estimated consistently. The proposed model and the estimation method are also illustrated with both simulated and real data, showing effective dimension-reduction in modelling and forecasting matrix time series.