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An alternative to explicitly modelling the heteroskedasticity is using a resampling method such as the wild bootstrap. Given that the studentized bootstrap, which standardizes the resampled statistic by its standard error, yields an asymptotic refinement, [13] heteroskedasticity-robust standard errors remain nevertheless useful.
Testing for groupwise heteroscedasticity can be done with the Goldfeld–Quandt test. [23] Due to the standard use of heteroskedasticity-consistent Standard Errors and the problem of Pre-test, econometricians nowadays rarely use tests for conditional heteroskedasticity. [6]
White test is a statistical test that establishes whether the variance of the errors in a regression model is constant: that is for homoskedasticity. This test, and an estimator for heteroscedasticity-consistent standard errors , were proposed by Halbert White in 1980. [ 1 ]
Generally, when testing for heteroskedasticity in econometric models, the best test is the White test. However, when dealing with time series data, this means to test for ARCH and GARCH errors. Exponentially weighted moving average (EWMA) is an alternative model in a separate class of exponential smoothing models. As an alternative to GARCH ...
The second test proposed in the paper is a nonparametric one and hence does not rely on the assumption that the errors have a normal distribution. For this test, a single regression model is fitted to the complete dataset. The squares of the residuals are listed according to the order of the pre-identified explanatory variable.
The test has been discussed in econometrics textbooks. [2] [3] Stephen Goldfeld and Richard E. Quandt raise concerns about the assumed structure, cautioning that the v i may be heteroscedastic and otherwise violate assumptions of ordinary least squares regression. [4]
In Stata, the command newey produces Newey–West standard errors for coefficients estimated by OLS regression. [13] In MATLAB, the command hac in the Econometrics toolbox produces the Newey–West estimator (among others). [14] In Python, the statsmodels [15] module includes functions for the covariance matrix using Newey–West.
Step 3: Select the equation with the highest R 2 and lowest standard errors to represent heteroscedasticity. Step 4: Perform a t-test on the equation selected from step 3 on γ 1 . If γ 1 is statistically significant, reject the null hypothesis of homoscedasticity.