GoldfeldQuandt

GoldfeldQuandt refers to the Goldfeld-Quandt test, a statistical method used to detect heteroskedasticity in linear regression models. Named after its developers, the test is particularly suited for situations in which the variance of the error term is believed to change in a systematic way with the ordering of observations, such as with an increasing level of an explanatory variable.

In practice, observations are first ordered by a presumed ordering variable. A central block of g observations is then omitted to avoid the region where variance is most likely to change. The remaining observations are split into two end groups. The variances of the regression residuals within these two groups, s1^2 and s2^2, are computed. The test statistic is the ratio of these variances (typically the larger variance divided by the smaller one), which under the null hypothesis of homoskedasticity follows an F distribution with degrees of freedom corresponding to the sizes of the two groups (one less than each group’s size). If the observed ratio exceeds the critical value at a chosen significance level, the null hypothesis of constant error variance is rejected, suggesting heteroskedasticity.

Variants of the test differ in how the central block size g is chosen and how the two end groups are formed. The Goldfeld-Quandt test is one of several econometric tools for assessing heteroskedasticity, alongside tests such as Breusch-Pagan and White. The method is especially common in cross-sectional and time-series regression settings where variance may systematically shift with an ordering variable.