Chi-square tests for multivariate normality with application to common stock prices

摘要: The theory of chi-square tests with data-dependent cells is applied to provide fit the family p-variate normal distributions. are bounded by hyperellipses (x-[Xbar])'S-1 (x-[Xbar]) = ci centered at sample mean [Xbar] and having shape deter-mined covariance matrix S. Pearson statistic these affine-invariant, has a null distribution not depending on true covariance, asymptotic critical points between those x2 (M-1) (M-2) when M employed. test insensitive lack symmetry, but peakedness, broad shoulders heavy tails easily discerned in cell counts. Multivariate normality logarithms relative prices common stocks, assumption finan-cial markets theory, studied using described here large data base.