Fourier methods for testing multivariate independence

Recently a power study of some popular tests for bivariate independence based on ranks has been conducted. An alternative class of tests appropriate for testing not only bivariate, but also multivariate independence is developed, and their small-sample performance is studied. The test statistics employ the familiar equation between the joint characteristic function and the product of component characteristic functions, and may be written in a closed form convenient for computer implementation. Simulations on a distribution-free version of the new test statistic show that the proposed method compares well to standard methods of testing independence via the empirical distribution function. The methods are applied to multivariate observations incorporating data from several major stock-market indices. Issues pertaining to the theoretical properties of the new test are also addressed.

[1]  Yongmiao Hong.  Testing for pairwise serial independence via the empirical distribution function , 1998 .

[2]  B. Rémillard,et al.  A Nonparametric Test of Serial Independence for Time Series and Residuals , 2001 .

[3]  Derek S. Cotterill,et al.  ON THE LIMITING DISTRIBUTION OF AND CRITICAL VALUES FOR THE HOEFFDING, BLUM, KIEFER, ROSENBLATT INDEPENDENCE CRITERION , 1985 .

[4]  Simos G. Meintanis,et al.  Tests for normal mixtures based on the empirical characteristic function , 2005, Comput. Stat. Data Anal..

[5]  N. Ushakov.  Selected Topics in Characteristic Functions , 1999 .

[6]  Wolfgang Kössler,et al.  Linear rank tests for independence in bivariate distributions - power comparisons by simulation , 2004, Comput. Stat. Data Anal..

[7]  Byron J. T. Morgan,et al.  Integrated squared error estimation of normal mixtures , 2004, Comput. Stat. Data Anal..

[8]  Runze Li,et al.  A multivariate version of Ghosh's T 3 -plot to detect non-multinormality , 1998 .

[9]  J. Kiefer,et al.  DISTRIBUTION FREE TESTS OF INDEPENDENCE BASED ON THE SAMPLE DISTRIBUTION FUNCTION , 1961 .

[10]  A. Ledford,et al.  Statistics for near independence in multivariate extreme values , 1996 .

[11]  S. Rachev,et al.  Testing Multivariate Symmetry , 1995 .

[12]  P. Lafaye de Micheaux,et al.  A multivariate empirical characteristic function test of independence with normal marginals , 2003 .

[13]  S. Coles,et al.  Modelling Extreme Multivariate Events , 1991 .

[14]  Tom Smith,et al.  A Test for Multivariate Normality in Stock Returns , 1993 .

[15]  T. W. Epps.  Tests for location-scale families based on the empirical characteristic function , 2005 .

[16]  Jun Yu.  Empirical Characteristic Function Estimation and Its Applications , 2003 .

[17]  S. Csörgo.  Testing for independence by the empirical characteristic function , 1985 .

[18]  Simos G. Meintanis,et al.  Invariant tests for symmetry about an unspecified point based on the empirical characteristic function , 2003 .

[19]  S. Meintanis.  Permutation tests for homogeneity based on the empirical characteristic function , 2005 .

[20]  A. Feuerverger,et al.  The Empirical Characteristic Function and Its Applications , 1977 .

[21]  Miklos Csorgo,et al.  On the limiting distribution of and critical values for the multivariate Cramér-von Mises , 1982 .

[22]  Oriol Roch,et al.  Testing the bivariate distribution of daily equity returns using copulas. An application to the Spanish stock market , 2006, Comput. Stat. Data Anal..

[23]  Byron J. T. Morgan,et al.  Integrated squared error estimation of Cauchy parameters , 2001 .

[24]  W. Hoeffding.  A Non-Parametric Test of Independence , 1948 .

[25]  A. Feuerverger,et al.  A Consistent Test for Bivariate Dependence , 1993 .

[26]  A. Kankainen,et al.  A consistent modification of a test for independence based on the empirical characteristic function , 1998 .