Eigen-Analysis for High-Dimensional Time Series Clustering

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

No 22/23, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: Cross-sectional structures and temporal tendency are important features of highdimensional time series. Based on eigen-analysis on sample covariance matrices, we propose a novel approach to identifying four popular structures of high-dimensional time series, which are grouped in terms of factor structures and stationarity. The proposed three-step method includes: (1) the ratio statistic of empirical eigenvalues; (2) a projected Augmented Dickey-Fuller Test; (3) a new unit-root test based on the largest empirical eigenvalues. We develop asymptotic properties for these three statistics to ensure the feasibility for the whole procedure. Finite sample performances are illustrated via various simulations. Our results are further applied to analyze U.S. mortality data, U.S. house prices and income, and U.S. sectoral employment, all of which possess cross-sectional dependence as well as non-stationary temporal dependence. It is worth mentioning that we also contribute to statistical justification for the benchmark paper by Lee and Carter (1992) in mortality forecasting.

Keywords: factor model; non-stationarity; sample covariance matrix; stationarity (search for similar items in EconPapers)
JEL-codes: C18 C32 C55 (search for similar items in EconPapers)
Pages: 69
Date: 2023
New Economics Papers: this item is included in nep-ecm and nep-ets
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