Heteroscedasticity - Detection

Detection

There are several methods to test for the presence of heteroscedasticity. Although tests for heteroscedasticity between groups can formally be considered as a special case of testing within regression models, some tests have structures specific to this case.

Tests in regression

• Park test (1966)
• Glejser test (1969)
• White test
• Breusch–Pagan test
• Goldfeld–Quandt test
• Cook–Weisberg test
• Harrison–McCabe test
• Brown–Forsythe test
• Levene test

Tests for grouped data

• F-test of equality of variances
• Cochran's C test
• Hartley's test

These tests consist of a test statistic (a mathematical expression yielding a numerical value as a function of the data), a hypothesis that is going to be tested (the null hypothesis), an alternative hypothesis, and a statement about the distribution of statistic under the null hypothesis.

Many introductory statistics and econometrics books, for pedagogical reasons, present these tests under the assumption that the data set in hand comes from a normal distribution. A great misconception is the thought that this assumption is necessary. Most of the methods of detecting heteroscedasticity outlined above modified for use even when the data do not come from a normal distribution. In many cases, this assumption can be relaxed, yielding a test procedure based on the same or similar test statistics but with the distribution under the null hypothesis evaluated by alternative routes: for example, by using asymptotic distributions which can be obtained from asymptotic theory, or by using resampling.