论文标题
张量因子模型中的等级确定
Rank Determination in Tensor Factor Model
论文作者
论文摘要
因子模型是高维时间序列的吸引力且有效的分析工具，在经济学，金融和统计中具有广泛的应用。本文制定了两个标准，用于确定张量因子模型的因子数量，其中观察到的张量时间序列的信号部分假设将塔克分解与核心张量作为因子张量。任务是确定核心张量的尺寸。提出的标准之一类似于模型选择的基于信息的标准，另一个是基于经常用于小组时间序列的因子分析中的连续特征值的比率的扩展。理论上的结果，包括足够的条件和收敛速率。结果包括矢量因子模型作为特殊情况，并具有额外的收敛速率。模拟研究为这两个标准提供了有希望的有限样本性能。
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.
