Heteroscedasticity

A heteroscedastic regression model is Model 6 where X is a diagonal matrix, the diagonal elements of which assume at least two different values. Hetero­scedasticity is a common occurrence in econometric applications and can often be detected by plotting the least squares residuals against time, the dependent variable, the regression mean, or any other linear combination of the independent variables. For example, Prais and Houthakker (1955) found that a variability of the residuals from a regression of food expenditure on income increases with income. In the subsequent subsections we shall con­sider various ways to parameterize the heteroscedasticity. We shall consider the estimation of the heteroscedasticity parameters as well as the regression coefficients. We shall also discuss tests for heteroscedasticity.

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