IN A RECENT ARTICLE in this Journal, Giaccotto and Ali [7] addressed several potential deficiencies in prior studies which investigated heteroskedasticity in the single index market model. Much of the previous work employed standard parametric tests for heteroskedasticity, such as the Goldfeld-Quandt, Bartlett, or Glejser tests, which lean heavily on the assumed normality of the disturbances, a potentially untenable assumption in light of the apparent leptokurtotic nature of returns. Moreover, some authors have employed alternative tests, such as the Goldfeld-Quandt peak test, on the ordinary least squares (OLS) residuals from market model regressions under the assumption of the independence of the OLS residuals when, in fact, these residuals are correlated by construction. Finally, the previous literature investigated only a small number of specific forms of heteroskedasticity whereas Giaccotto and Ali [7] suggested the virtues of tests which have power against a variety of alternatives. These considerations led Giaccotto and Ali to consider alternative rank and robust tests which have good power characteristics.1 Since these test statistics require the use of independent observations, Giaccotto and Ali observed that OLS residuals should not be used in such tests since they are correlated and, hence, dependent. The authors instead employed recursive residuals which were introduced by Brown and Durbin [2] and since have been studied extensively in Brown, Durbin, and Evans [3], Hedayat and Robson [11], Harvey and Phillips [10], Harvey and Collier [9], Godolphin and DeTullio [8], Dufour [4], and Garbade [6]. These recursive residuals are standardized one step ahead prediction errors which by construction are mutually uncorrelated. Giaccotto and Ali concluded that this orthogonality property makes recursive residuals appropriate for the construction of the aforementioned test statistics. Unfortunately, this unwarranted conclusion involves an elementary flaw in statistical reasoning since uncorrelated random variables that are not normally distributed are not necessarily independent. This simple observation renders their claims involving the distribution-free nature of their tests incorrect. In fact, it is not clear whether any of their test statistics possess well-defined distributions in large samples when based on recursive residuals.