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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.
To test for constant variance one undertakes an auxiliary regression analysis: this regresses the squared residuals from the original regression model onto a set of regressors that contain the original regressors along with their squares and cross-products. [3] One then inspects the R 2.
Thus, regression analysis using heteroscedastic data will still provide an unbiased estimate for the relationship between the predictor variable and the outcome, but standard errors and therefore inferences obtained from data analysis are suspect. Biased standard errors lead to biased inference, so results of hypothesis tests are possibly wrong.
A Newey–West estimator is used in statistics and econometrics to provide an estimate of the covariance matrix of the parameters of a regression-type model where the standard assumptions of regression analysis do not apply. [1] It was devised by Whitney K. Newey and Kenneth D. West in 1987, although there are a number of later variants.
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.
In this variant, the dependent variable in the auxiliary regression is just the squared residual from the Step 1 regression, ^, and the test statistic is from the auxiliary regression. As Koenker notes (1981, page 111), while the revised statistic has correct asymptotic size its power "may be quite poor except under idealized Gaussian conditions."
[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.
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 ...