An omnibus test for heteroscedasticity using radial stationarity and data depth

Abstract

The classical linear regression model is a very well-known and widely used statistical method. One of the assumptions on which the model’s validity rests is that of constant error variance (homoscedasticity). Thus, heteroscedasticity testing plays an important role in linear regression model diagnostics. This study proposes an omnibus test for heteroscedasticity in the classical linear regression model using the notion of radial stationarity about the centre of the explanatory variable space, combined with the notion of data depth. The test procedure consists of constructing a spatially ordered series of residuals (after removing the deepest observations) that is then tested for weak stationarity. Monte Carlo simulations show that, when the Priestley-Subba Rao method is used as the stationarity test, the resulting ‘radial stationarity’ test outperforms the Breusch-Pagan Test and White’s Test in terms of average excess power over size under a variety of heteroscedastic alternatives, in some cases by a wide margin. The size of the proposed test is not robust under non-normality, however, and two nonparametric stationarity tests performed poorly in the simulations.