SFB 303 Discussion Paper No. A - 248

Author: Dutta, Jayasri, and Asad Zaman
Title: What Do tests for Heteroskedasticity Detect?
Abstract: A test is said to detect an alternative hypothesis if it is unbiased against it, at all levels and all sample sizes. It is a robust test if this property is true for a large class of null distributions. This approach allows for method of comparison of tests which can be carried out for finite samples as well as in asymptotic behavior. We use this method to compare the properties of several methods of testing for heteroskedasticity, emphasizing on the possibility of testing for nonspecific heteroskedasticity. We show that a robust test for non-specific heteroskedasticity is impossible. Usual tests, both exact and asymptotic, usually retain robustness, while giving up non-specifity. We demonstrate and apply methods which characterize, for a large class, the directions which such tests detect. Alternatively, one may give up robustness in order to detect all departures from the null. We show that such a test can be developed along lines suggested by Pitman (1938). The test is distribution specific. The test statistic for the normal distribution writes as the ratio of arithmetic and geometric means of the squared errors.
Creation-Date: August 1989
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