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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.
Heteroscedasticity-consistent standard errors (HCSE), while still biased, improve upon OLS estimates. [2] HCSE is a consistent estimator of standard errors in regression models with heteroscedasticity. This method corrects for heteroscedasticity without altering the values of the coefficients.
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.
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.
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.
Weighted least squares (WLS), also known as weighted linear regression, [1] [2] is a generalization of ordinary least squares and linear regression in which knowledge of the unequal variance of observations (heteroscedasticity) is incorporated into the regression.
Suppose that we estimate the regression model = + +, and obtain from this fitted model a set of values for ^, the residuals. Ordinary least squares constrains these so that their mean is 0 and so, given the assumption that their variance does not depend on the independent variables, an estimate of this variance can be obtained from the average of the squared values of the residuals.
If a visual examination suggests, for example, the possible presence of heteroscedasticity (a relationship between the variance of the model errors and the size of an independent variable's observations), then statistical tests can be performed to confirm or reject this hunch; if it is confirmed, different modeling procedures are called for.