Independence Test for High Dimensional Random Vectors

G. Pan, J. Gao (), Y. Yang and M. Guo
Authors registered in the RePEc Author Service: Jiti GAO and Jassduke Gao

No 1/12, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

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 (search for similar items in EconPapers)
JEL-codes: C12 C21 C22 (search for similar items in EconPapers)
Pages: 41 pages
Date: 2012-01-20
New Economics Papers: this item is included in nep-ecm and nep-ets
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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