Eigen-Analysis for High-Dimensional Time Series Clustering

Cross-sectional structures and temporal tendency are important features of high dimensional 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.