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

Xinyu Zhang and Howell Tong

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: 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.

Keywords: bootstrap; inference; limiting distribution; PCA; portfolio management; time series (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 23 pages
Date: 2022-04-01
New Economics Papers: this item is included in nep-ecm and nep-ets
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in Journal of the Royal Statistical Society. Series A: Statistics in Society, 1, April, 2022, 185(2), pp. 543 - 565. ISSN: 0964-1998

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