张量因子模型中的秩确定
Rank Determination in Tensor Factor Model
摘要：
因子模型是高维时间序列的一种有效分析工具，在经济、金融、统计等领域有着广泛的应用。本文发展了两个标准的张量因子模型的因子的数量的确定的信号部分的观测张量时间序列假设Tucker分解的核心张量作为因子张量。任务是确定核张量的维数。其中一个准则类似于基于信息的模型选择准则，另一个准则是对面板时间序列因子分析中常用的基于连续特征值比值的方法的扩展。理论上的结果，包括充分条件和收敛速度。结果包括向量因子模型作为特殊情况，具有额外的收敛速度。仿真研究提供了有前途的有限样本性能的两个标准。
英文摘要：
Factor model is an appealing and effective analytic tool for high-dimensional time series, with a wide range of applications in economics, finance and statistics. This paper develops two criteria for the determination of the number of factors for tensor factor models where the signal part of an observed tensor time series assumes a Tucker decomposition with the core tensor as the factor tensor. The task is to determine the dimensions of the core tensor. One of the proposed criteria is similar to information based criteria of model selection, and the other is an extension of the approaches based on the ratios of consecutive eigenvalues often used in factor analysis for panel time series. Theoretically results, including sufficient conditions and convergence rates, are established. The results include the vector factor models as special cases, with an additional convergence rates. Simulation studies provide promising finite sample performance for the two criteria.
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