Factor Model Based Estimation for High Dimensional Reduced-Rank Time Series
针对高维多响应时间序列，提出一种基于因子模型的降秩系数矩阵估计方法，并构造两个检验统计量用于序列依赖性检验，模拟和实证表明方法更有效。
High-dimensional time series are very common in reality. Analyzing each series separately may not be a good strategy, as it may miss some important information and result in a less optimal outcome. Even worse, in some cases, it may not even provide an answer to the question of interest. Reduced-rank model is an important tool for joint analysis of high-dimensional multiple-response time series. In this paper, we develop a new and powerful method for estimating the coefficient matrix of a multiple-response reduced-rank time series model based on factor models. With the help of the estimated factors, we also propose two statistics for testing the dependence of high-dimensional time series. Asymptotic results for the proposed estimators and tests are established. Intensive simulation studies show that the proposed procedure is more powerful than its alternatives. We also apply the proposed method to a real dataset to illustrate its usefulness in solving real-life problems.