To deal with the factor analysis for high-dimensional stationary time series, this paper suggests a novel method that integrates three ideas. First, based on the eigenvalues of a non-negative definite matrix, we propose a new approach for consistently determining the number of factors. The proposed method is computationally efficient with a single step procedure, especially when both weak and strong factors exist in the factor model. Second, a fresh measurement of the difference between the factor loading matrix and its estimate is recommended to overcome the nonidentifiability of the loading matrix due to any geometric rotation. The asymptotic results of our proposed method are also studied under this measurement, which enjoys “blessing of dimensionality.” Finally, with the estimated factors, the latent vector autoregressive (VAR) model is analyzed such that the convergence rate of the estimated coefficients is as fast as when the samples of VAR model are observed. In support of our results on consistency and computational efficiency, the finite sample performance of the proposed method is examined by simulations and the analysis of one real data example.

中文翻译：

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高维时间序列的因子分析：一致估计和高效计算

针对高维平稳时间序列的因子分析，本文提出了一种融合三种思想的新方法。首先，基于非负定矩阵的特征值，我们提出了一种新的方法来一致地确定因子的数量。所提出的方法在单步过程中计算效率很高，特别是当因子模型中同时存在弱因子和强因子时。其次，建议重新测量因子加载矩阵与其估计之间的差异，以克服由于任何几何旋转导致的加载矩阵的不可识别性。我们提出的方法的渐近结果也在这种测量下进行了研究，它享有“维度的祝福”。最后，通过估计的因素，对潜在向量自回归 (VAR) 模型进行分析，使得估计系数的收敛速度与观察 VAR 模型的样本时一样快。为了支持我们关于一致性和计算效率的结果，通过模拟和一个真实数据示例的分析来检查所提出方法的有限样本性能。