Asymptotic Theory of Principal Component Analysis for High-Dimensional Time Series Data under a Factor Structure

Matteo Barigozzi

Papers from arXiv.org

Abstract: 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.

Date: 2022-11, Revised 2025-07
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