Spiked Eigenvalues of High-Dimensional Separable Sample Covariance Matrices

40 Pages Posted: 17 Dec 2019

See all articles by Bo Zhang

Bo Zhang

Monash University

Jiti Gao

Monash University - Department of Econometrics & Business Statistics

Guangming Pan

Nanyang Technological University (NTU)

Yanrong Yang

The Australian National University

Date Written: December 2, 2019

Abstract

This paper establishes asymptotic properties for spiked empirical eigenvalues of sample co- variance matrices for high-dimensional data with both cross-sectional dependence and a dependent sample structure. A new finding from the established theoretical results is that spiked empirical eigenvalues will reflect the dependent sample structure instead of the cross-sectional structure under some scenarios, which indicates that principal component analysis (PCA) may provide inaccurate inference for cross-sectional structures. An illustrated example is provided to show that some commonly used statistics based on spiked empirical eigenvalues mis-estimate the true number of common factors. As an application of high-dimensional time series, we propose a test statistic to distinguish the unit root from the factor structure and demonstrate its effective finite sample performance on simulated data. Our results are then applied to analyze OECD healthcare expenditure data and U.S. mortality data, both of which possess cross-sectional dependence as well as non-stationary temporal dependence. It is worth mentioning that we contribute to statistical justification for the benchmark paper by Lee and Carter in mortality forecasting.

Keywords: Factor Model; High-Dimensional Data; Principal Component Analysis; Spiked Empirical Eigenvalue

JEL Classification: C21; C32; C55

Suggested Citation

Zhang, Bo and Gao, Jiti and Pan, Guangming and Yang, Yanrong, Spiked Eigenvalues of High-Dimensional Separable Sample Covariance Matrices (December 2, 2019). Available at SSRN: https://ssrn.com/abstract=3496388 or http://dx.doi.org/10.2139/ssrn.3496388

Bo Zhang

Monash University ( email )

900 Dandenong Road
Caulfield East, 3145
Australia

Jiti Gao (Contact Author)

Monash University - Department of Econometrics & Business Statistics ( email )

900 Dandenong Road
Caulfield East, Victoria 3145
Australia
61399031675 (Phone)
61399032007 (Fax)

HOME PAGE: http://www.jitigao.com

Guangming Pan

Nanyang Technological University (NTU) ( email )

S3 B2-A28 Nanyang Avenue
Singapore, 639798
Singapore

Yanrong Yang

The Australian National University ( email )

Canberra, Australian Capital Territory 2601
Australia

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