Abstract
To address the drawbacks of the traditional Parker test in multivariate linear models: the process is cumbersome and computationally intensive, we propose a new heteroscedasticity test. A new heteroskedasticity test is proposed using the fitted values of the samples as new explanatory variables, reconstructing the regression model, and giving a new heteroskedasticity test based on the significance test of the coefficients, it is also compared with the existing Parker test which is improved using the principal component idea. Numerical simulations and empirical analyses show that the improved Parker test with the fitted values of the samples proposed in this paper is superior.
Highlights
A basic assumption of classical linear regression analysis is that the random error terms of the model μi are homoskedastic, i.e. they have the same variance σ 2
A new heteroskedasticity test is proposed using the fitted values of the samples as new explanatory variables, reconstructing the regression model, and giving a new heteroskedasticity test based on the significance test of the coefficients, It is compared with the existing Parker test which is improved using the principal component idea
We propose to use the sample fitting value yas the new explanatory variable to establish the regression equation with the residual logarithm, and compare the two methods with the Parker test improved by the principle component idea to compare the effectiveness and simplicity of the two methods
Summary
A basic assumption of classical linear regression analysis is that the random error terms of the model μi are homoskedastic, i.e. they have the same variance σ 2. On the premise of no loss of sample information, this paper uses the sample fitting value as a new explanatory variable to establish a regression model, carries out the significance test of the coefficient, and gives a new heteroscedasticity test method, which simplifies the steps of heteroscedasticity test for the multiple linear regression model. It is compared with Tan Xin’s improved Parker’s test. To ensure the completeness of the study, a brief introduction to the definition of heteroskedasticity and the traditional Parker test is given below
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