Principal Component Analysis for High-Dimensional Approximate Factor Models in Time Series: Assumptions, Asymptotic Theory, and Identification

We consider estimation of large approximate factor models in high-dimensional panels of stationary time series using Principal Component Analysis (PCA). We review the key results establishing the necessary and sufficient conditions for consistency and asymptotic normality of the estimators. We compare two equivalent approaches to PCA and present the asymptotic properties associated with each formulation. Special emphasis is placed on identification, where we discuss the restrictions required to uniquely determine factors and loadings and examine their consequences for statistical inference.