Asymptotic properties of correlation-based principal component analysis

Jungjun Choi and Xiye Yang

Journal of Econometrics, 2022, vol. 229, issue 1, 1-18

Abstract: It is a common practice to conduct principal component analysis (PCA) using standardized data, which is equivalent to applying PCA to the correlation matrix rather than the covariance matrix. Yet little research has been done about such differences in the context of high frequency data. This paper bridges this gap. We derive the analytical forms of the asymptotic biases and variances for the estimators of the integrated eigenvalues and eigenvectors. Furthermore, we propose a novel jackknife-type estimator of the asymptotic variance of the integrated volatility functional estimator. This new variance estimator shows much better finite sample performances compared to other existing ones. This paper also proposes several statistical tests for some commonly tested hypotheses in the literature. Simulation results show that one will get misleading results if one uses the analytical results of the covariance case when applying PCA on the correlation matrix.

Keywords: Correlation matrix; Eigenvalue; Eigenvector; High frequency; Principal component; Standardized data (search for similar items in EconPapers)
JEL-codes: C38 (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:229:y:2022:i:1:p:1-18

DOI: 10.1016/j.jeconom.2021.08.003

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