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Eigen-Analysis for High-Dimensional Time Series Clustering

Author

Listed:
  • Bo Zhang
  • Jiti Gao
  • Guangming Pan
  • Yanrong Yang

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.

Suggested Citation

  • Bo Zhang & Jiti Gao & Guangming Pan & Yanrong Yang, 2023. "Eigen-Analysis for High-Dimensional Time Series Clustering," Monash Econometrics and Business Statistics Working Papers 22/23, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2023-22
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    File URL: https://www.monash.edu/business/ebs/research/publications/ebs/2023/wp22-2023.pdf
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    References listed on IDEAS

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    1. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    2. Bhansali, R.J. & Giraitis, L. & Kokoszka, P.S., 2007. "Convergence of quadratic forms with nonvanishing diagonal," Statistics & Probability Letters, Elsevier, vol. 77(7), pages 726-734, April.
    3. Alexei Onatski & Chen Wang, 2021. "Spurious Factor Analysis," Econometrica, Econometric Society, vol. 89(2), pages 591-614, March.
    4. Seung C. Ahn & Alex R. Horenstein, 2013. "Eigenvalue Ratio Test for the Number of Factors," Econometrica, Econometric Society, vol. 81(3), pages 1203-1227, May.
    5. Alexei Onatski, 2010. "Determining the Number of Factors from Empirical Distribution of Eigenvalues," The Review of Economics and Statistics, MIT Press, vol. 92(4), pages 1004-1016, November.
    6. Baik, Jinho & Silverstein, Jack W., 2006. "Eigenvalues of large sample covariance matrices of spiked population models," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1382-1408, July.
    7. Bai, Jushan, 2004. "Estimating cross-section common stochastic trends in nonstationary panel data," Journal of Econometrics, Elsevier, vol. 122(1), pages 137-183, September.
    8. Jianqing Fan & Jianhua Guo & Shurong Zheng, 2022. "Estimating Number of Factors by Adjusted Eigenvalues Thresholding," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(538), pages 852-861, April.
    9. Lam, Clifford & Yao, Qiwei, 2012. "Factor modeling for high-dimensional time series: inference for the number of factors," LSE Research Online Documents on Economics 45684, London School of Economics and Political Science, LSE Library.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    factor model; non-stationarity; sample covariance matrix; stationarity;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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