论文标题
部分可观测时空混沌系统的无模型预测
Asymptotic Theory of Principal Component Analysis for High-Dimensional Time Series Data under a Factor Structure
论文作者
论文摘要
我们回顾了$ n $固定时间序列面板的大近似因子模型的主成分（PC）估计，我们提供了估计量的渐近性能的新推导，这些估计剂的渐变性是在最小的假设集中衍生而成的，仅需要第四阶矩的存在。为此，我们还回顾了样品协方差矩阵的均值一致性的各种原始条件的各种替代性。最后，我们详细讨论了识别负载和因素的问题及其对推理的影响。
We review Principal Components (PC) estimation of a large approximate factor model for a panel of $n$ stationary time series and we provide new derivations of the asymptotic properties of the estimators, which are derived under a minimal set of assumptions requiring only the existence of 4th order moments. To this end, we also review various alternative sets of primitive sufficient conditions for mean-squared consistency of the sample covariance matrix. Finally, we discuss in detail the issue of identification of the loadings and factors as well as its implications for inference.
