Independence Test for High Dimensional Random Vectors

41 Pages Posted: 22 Mar 2012

See all articles by Jiti Gao

Jiti Gao

Monash University - Department of Econometrics & Business Statistics

G. Pan

affiliation not provided to SSRN

M. Guo

affiliation not provided to SSRN

Date Written: January 20, 2012

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.

Keywords: Independence test, cross--sectional dependence, empirical spectral distribution, characteristic function, Marcenko-Pastur Law

JEL Classification: C12, C21, C22

Suggested Citation

Gao, Jiti and Pan, G. and Guo, M., Independence Test for High Dimensional Random Vectors (January 20, 2012). Available at SSRN: https://ssrn.com/abstract=2027295 or http://dx.doi.org/10.2139/ssrn.2027295

Jiti Gao (Contact Author)

Monash University - Department of Econometrics & Business Statistics ( email )

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Caulfield East, Victoria 3145
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HOME PAGE: http://www.jitigao.com

G. Pan

affiliation not provided to SSRN

M. Guo

affiliation not provided to SSRN

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