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Asymptotic theory of principal component analysis for time series data with cautionary comments

Zhang, Xinyu and Tong, Howell (2022) Asymptotic theory of principal component analysis for time series data with cautionary comments. Journal of the Royal Statistical Society. Series A: Statistics in Society, 185 (2). 543 - 565. ISSN 0964-1998

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Identification Number: 10.1111/rssa.12793


Principal component analysis (PCA) is a most frequently used statistical tool in almost all branches of data science. However, like many other statistical tools, there is sometimes the risk of misuse or even abuse. In this paper, we highlight possible pitfalls in using the theoretical results of PCA based on the assumption of independent data when the data are time series. For the latter, we state with proof a central limit theorem of the eigenvalues and eigenvectors (loadings), give direct and bootstrap estimation of their asymptotic covariances, and assess their efficacy via simulation. Specifically, we pay attention to the proportion of variation, which decides the number of principal components (PCs), and the loadings, which help interpret the meaning of PCs. Our findings are that while the proportion of variation is quite robust to different dependence assumptions, the inference of PC loadings requires careful attention. We initiate and conclude our investigation with an empirical example on portfolio management, in which the PC loadings play a prominent role. It is given as a paradigm of correct usage of PCA for time series data.

Item Type: Article
Official URL:
Additional Information: © 2022 Royal Statistical Society
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 27 Jan 2022 16:57
Last Modified: 17 May 2024 00:06

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