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CLT for Largest Eigenvalues and Unit Root Tests for High-Dimensional Nonstationary Time Series

Author

Listed:
  • Bo Zhang
  • Guangming Pan
  • Jiti Gao

Abstract

This paper first considers some testing issues for a vector of high-dimensional time series before it establishes a joint distribution for the largest eigenvalues of the corresponding co-variance matrix associated with the high-dimensional time series for the case where both the dimensionality of the time series and the length of time series go to infinity. As an application, a new unit root test for a vector of high-dimensional time series is proposed and then studied both theoretically and numerically to show that existing unit tests for the fixed-dimensional case are not applicable

Suggested Citation

  • Bo Zhang & Guangming Pan & Jiti Gao, 2016. "CLT for Largest Eigenvalues and Unit Root Tests for High-Dimensional Nonstationary Time Series," Monash Econometrics and Business Statistics Working Papers 11/16, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2016-11
    as

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    File URL: http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp11-16.pdf
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    References listed on IDEAS

    as
    1. Choi, In, 2001. "Unit root tests for panel data," Journal of International Money and Finance, Elsevier, vol. 20(2), pages 249-272, April.
    2. Chang, Yoosoon, 2004. "Bootstrap unit root tests in panels with cross-sectional dependency," Journal of Econometrics, Elsevier, vol. 120(2), pages 263-293, June.
    3. 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.
    4. Guangming Pan & Jiti Gao & Yanrong Yang, 2014. "Testing Independence Among a Large Number of High-Dimensional Random Vectors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 600-612, June.
    5. Im, Kyung So & Pesaran, M. Hashem & Shin, Yongcheol, 2003. "Testing for unit roots in heterogeneous panels," Journal of Econometrics, Elsevier, vol. 115(1), pages 53-74, July.
    6. Ningning Xia & Zhidong Bai, 2015. "Functional CLT of eigenvectors for large sample covariance matrices," Statistical Papers, Springer, vol. 56(1), pages 23-60, February.
    7. Levin, Andrew & Lin, Chien-Fu & James Chu, Chia-Shang, 2002. "Unit root tests in panel data: asymptotic and finite-sample properties," Journal of Econometrics, Elsevier, vol. 108(1), pages 1-24, May.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    asymptotic normality; largest eigenvalue; linear process; unit root test;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • 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

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