An Application of the Chi-Squared Goodness-of-Fit Test to Discrete Common Stock Returns
提出一种改进的卡方拟合优度检验方法（中心化法），用于检验离散股票收益率是否服从正态或混合正态分布，显著降低了传统方法的偏差，对低价低波动股票尤其有效。
This article presents the "centered" method for establishing cell boundaries in the X 2 goodness-of-fit test, which when applied to common stock returns significantly reduces the high bias of the test statistic associated with the traditional Mann–Wald equiprobable approach. A modified null hypothesis is proposed to incorporate explicitly the usually implicit assumption that the observed discrete returns are "approximated" by the hypothesized continuous density. Simulation results indicate extremely biased X 2 values resulting from the traditional approach, particularly for low-priced and low volatile stocks. Daily stock returns for 114 firms are tested to determine whether they are approximated by a normal or one of several normal mixture densities. Results indicate a significantly higher degree of fit than that reported elsewhere to date.