Spiked Eigenvalues of High-Dimensional Separable Sample Covariance Matrices

Bo Zhang, Jiti Gao, Guangming Pan () and Yanrong Yang ()

No 31/19, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: This paper establishes asymptotic properties for spiked empirical eigenvalues of sample covariance 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 misestimate 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 [25] in mortality forecasting.

Keywords: factor model; high-dimensional data; principal component analysis; spiked empirical eigenvalue. (search for similar items in EconPapers)
JEL-codes: C21 C32 C55 (search for similar items in EconPapers)
Pages: 40
Date: 2019
New Economics Papers: this item is included in nep-ecm and nep-ore
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