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Independence Test for High Dimensional Random Vectors

Author

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  • G. Pan
  • J. Gao
  • Y. Yang
  • M. Guo

Abstract

This paper proposes a new mutual independence test for a large number of high dimensional random vectors. The test statistic is based on the characteristic function of the empirical spectral distribution of the sample covariance matrix. The asymptotic distributions of the test statistic under the null and local alternative hypotheses are established as dimensionality and the sample size of the data are comparable. We apply this test to examine multiple MA(1) and AR(1) models, panel data models with some spatial cross-sectional structures. In addition, in a flexible applied fashion, the proposed test can capture some dependent but uncorrelated structures, for example, nonlinear MA(1) models, multiple ARCH(1) models and vandermonde matrices. Simulation results are provided for detecting these dependent structures. An empirical study of dependence between closed stock prices of several companies from New York Stock Exchange (NYSE) demonstrates that the feature of cross-sectional dependence is popular in stock markets

Suggested Citation

  • G. Pan & J. Gao & Y. Yang & M. Guo, 2012. "Independence Test for High Dimensional Random Vectors," Monash Econometrics and Business Statistics Working Papers 1/12, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2012-1
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    File URL: http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp1-12.pdf
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    References listed on IDEAS

    as
    1. Silverstein, J. W., 1995. "Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 331-339, November.
    2. Jia Chen & Jiti Gao & Degui Li, 2009. "A New Diagnostic Test for Cross-Section Independence in Nonparametric Panel Data Model," School of Economics and Public Policy Working Papers 2009-16, University of Adelaide, School of Economics and Public Policy.
    3. Hsiao, Cheng & Pesaran, M. Hashem & Pick, Andreas, 2007. "Diagnostic Tests of Cross Section Independence for Nonlinear Panel Data Models," IZA Discussion Papers 2756, Institute of Labor Economics (IZA).
    4. M. Hashem Pesaran, 2021. "General diagnostic tests for cross-sectional dependence in panels," Empirical Economics, Springer, vol. 60(1), pages 13-50, January.
    5. Jianqing Fan & Jinchi Lv & Lei Qi, 2011. "Sparse High-Dimensional Models in Economics," Annual Review of Economics, Annual Reviews, vol. 3(1), pages 291-317, September.
    6. Chen, Jia & Gao, Jiti & Li, Degui, 2012. "A New Diagnostic Test For Cross-Section Uncorrelatedness In Nonparametric Panel Data Models," Econometric Theory, Cambridge University Press, vol. 28(5), pages 1144-1163, October.
    7. Hsiao, Cheng & Pesaran, M. Hashem & Pick, Andreas, 2007. "Diagnostic Tests of Cross Section Independence for Nonlinear Panel Data Models," IZA Discussion Papers 2756, Institute of Labor Economics (IZA).
    8. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    9. Dozier, R. Brent & Silverstein, Jack W., 2007. "On the empirical distribution of eigenvalues of large dimensional information-plus-noise-type matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(4), pages 678-694, April.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Hyodo, Masashi & Nishiyama, Takahiro & Pavlenko, Tatjana, 2020. "Testing for independence of high-dimensional variables: ρV-coefficient based approach," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    2. Joel Bun & Jean-Philippe Bouchaud & Marc Potters, 2016. "Cleaning large correlation matrices: tools from random matrix theory," Papers 1610.08104, arXiv.org.
    3. Feng, Long & Zhang, Xiaoxu & Liu, Binghui, 2020. "Multivariate tests of independence and their application in correlation analysis between financial markets," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    4. Bodnar, Taras & Dette, Holger & Parolya, Nestor, 2019. "Testing for independence of large dimensional vectors," MPRA Paper 97997, University Library of Munich, Germany, revised May 2019.

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    More about this item

    Keywords

    Independence test; cross-sectional dependence; empirical spectral distribution; characteristic function; Marcenko-Pastur Law;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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