Abstract
A highdimensional $r$factor model for an $n$dimensional vector time series is characterised by the presence of a large eigengap (increasing with $n$) between the $r$th and the $(r+1)$th largest eigenvalues of the covariance matrix. Consequently, Principal Component (PC) analysis is the most popular estimation method for factor models and its consistency, when $r$ is correctly estimated, is wellestablished in the literature. However, popular factor number estimators often suffer from the lack of an obvious eigengap in empirical eigenvalues and tend to overestimate $r$ due, for example, to the existence of nonpervasive factors affecting only a subset of the series. We show that the errors in the PC estimators resulting from the overestimation of $r$ are nonnegligible, which in turn lead to the violation of the conditions required for factorbased large covariance estimation. To remedy this, we propose new estimators of the factor model based on scaling the entries of the sample eigenvectors. We show both theoretically and numerically that the proposed estimators successfully control for the overestimation error, and investigate their performance when applied to risk minimisation of a portfolio of financial time series.
Original language  English 

Pages (fromto)  28922921 
Number of pages  30 
Journal  Electronic Journal of Statistics 
Volume  14 
Issue number  2 
DOIs  
Publication status  Published  31 Aug 2020 
Keywords
 factor models
 principal component analysis
 sample eigenvectors
 facator number
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Dr Haeran Cho
 School of Mathematics  Associate Professor in Statistics
 Statistical Science
 Statistics
Person: Academic , Member