Research On The Heteroscedasticity Test Methods Of Linear Regression Model

One of the important assumptions of the classical linear regression model is that the random error term has homoskedasticity.However,in most cases,the variance of the random error term in the model is not completely equal,that is to say,this assumption is not necessarily true.When heteroscedasticity exists in the model,if the ordinary least square method is still used for parameter estimation,it will have serious consequences,that is,the parameter estimator will be invalid,the significance test of the variable will be meaningless,the prediction of the model will fail and so on.Therefore,it is very important to choose the appropriate heteroscedasticity test method.Based on the traditional heteroscedasticity test methods,this paper explores and studies the shortcomings of the existing heteroscedasticity test methods,presents two improved heteroscedasticity test methods,and verifies the effects of the improved heteroscedasticity test methods through simulation data and empirical analysis.Firstly,the paper proposes an improved White test method.In the heteroscedasticity test of multiple linear regression models with more explanatory variables,the auxiliary regression model constructed by the traditional White test has more parameters to be estimated,which results in the loss of the degrees of freedom of the model.Based on this problem,the paper proposes to use the multiple correlation coefficient method to empower the explanatory variables,and to use the comprehensive index to establish a new auxiliary regression model for the heteroscedasticity test.The simulation data and example analysis show that this method is superior to the traditional method.Secondly,the paper proposes an improved Park test method.It is focused on the tradictional Park test here.Aim at solving a series of problems caused by the method in testing heteroscedasticity of multiple linear regression models,including heavy workload,cumbersome calculation and inaccurate heteroscedasticity model,the idea of using principle component analysis is put forward.A heteroscedasticity model is proposed for all the obtained aggregative indicators by using the principle of the distribution function of independent and identically distributed random variables,and different forms of data conditions are studied.According to the significance test of coefficients,a new method of testing heteroscedasticity is given.The simulation data and example analysis show that the new test method calculates faster and more accurate.Finally,the suitability of the improved White test method and the improved Park test method is compared by random simulation tests in three different forms of heteroscedasticity.The results show that,under certain conditions,if the study only needs to test whether there is heteroscedasticity in the model,the improved White test method can be used;if not only the heteroscedasticity in the model needs to be tested but also the specific expression of heteroscedasticity needs to be known in the study,an improved Park test method can be used.