An Application of the Chi-Squared Goodness-of-Fit Test to Discrete Common Stock Returns
卡方拟合优度检验在离散普通股收益中的应用AI 解读 ↓
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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.