The Handling Of Heteroscedastic Data In Regression Model

One of the important hypotheses of classical linear regression model is that the random disturbances have equal variance. However in most economic phenomena, this kind of hypothesis is not necessary true. Sometimes the disturbances vary with the observations. This is called heteroscedasticity. The model which has such kind of property is referred to as heteroscedastic regression model. If it is estimated by the method of OLS, it will bring about serious effect: the variances of the parameter estimators are not the least, and the accuracy of estimation and prediction decreases. Thus, it is of great significance to study the hypothesis testing of heteroscedasticity and statistical inference for the regression models with heteroscedasticity.In the first part of this article, the problem of heteroscedasticity is put forward. The serious effect is also stated.In the first section of the second part, several commonly cited testing methods are introduced, such as graph method, Spearman rank correlation coefficients test, Park test, Glejser test and Goldfeld-Quandt test. As Goldfeld-Quandt test can only be applied to one independent variable, it is generalized in the second section. It shows that, in Multivariate situation, the data can be arranged according to their principle components. But there should be a premise: the disturbances of the lower data group should have equal variance and those of the higher data group have the same variance. Otherwise the test result may be incorrect. It is worth researching how to choose the best testing method according to specific situation. In the third section three different forms of heteroscedasticity are used in the random simulation and then Park test, Glejser test and Goldfeld-Quandt test are comparedAlthough the existence of heteroscedasticity does not destroy the unbiasedness of the OLS estimators, the variances become larger. Thus, it makes the hypothesis testing unreliable. So, if heteroscedasticity is found exist through hypothesis testing, it should be dealt with in a suitable way. In the third part, the article mainly gives the methods to deal with the heteroscedasticity in different conditions.Using different methods to cope with heteroscedasticity may result in different models. Although these models can eliminate the heteroscedasticity, it is still necessary to make a further study to decide which model is much better and more effective. In the fourth part of this article, one real example is given. Firstly, several methods are used to test if there is heteroscedasticity in the data. Then some variance stabilizing transformation methods are applied to the data. Finally, it is pointed out that the least squares fitting may be used to the transformed data. Then goodness of fit is used to decide which model is better.The last part makes a brief conclusion of the article and points out that there are still some problems worth being further studied.