A Comparison of Tests for Heteroscedasticity

Abstract

We study the relationship, the size, the power, the sensitivity to high leverage, outliers and the normal error distribution of eight likelihood ratio and score tests for heteroscedasticity. Four versions of likelihood ratio tests are investigated which include the ordinary likelihood ratio test, the conditional likelihood ratio test obtained from Honda's conditional likelihood function, the residual likelihood ratio test derived from Verbyla's residual likelihood function and the modified likelihood ratio test adapted from Simonoff and Tsai. Furthermore, four score tests are examined which contain Breusch and Pagan's score test and its Studentized version (Koenker's score test), Verbyla's score test and the White score test which has been adopted by the SAS Institute. For normal errors, Monte Carlo results show that Verbyla's residual likelihood ratio test holds its null size well and is more powerful than other tests. For long-tailed or contaminated error distributions, Koenker's score test holds its null size better than other tests. In addition, Breusch and Pagan's and Verbyla's score tests are robust against high leverages. Finally, Monte Carlo studies show that Koenker's test outperforms White's test and should be used routinely in place of White's test. An example is presented to illustrate the test statistics.