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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.
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.
This test, and an estimator for heteroscedasticity-consistent standard errors, were proposed by Halbert White in 1980. [1] These methods have become widely used, making this paper one of the most cited articles in economics.
In Julia, the CovarianceMatrices.jl package [11] supports several types of heteroskedasticity and autocorrelation consistent covariance matrix estimation including Newey–West, White, and Arellano. In R , the packages sandwich [ 6 ] and plm [ 12 ] include a function for the Newey–West estimator.
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 a sample of T residuals under the null hypothesis of no ARCH errors, the test statistic T'R² follows distribution with q degrees of freedom, where ′ is the number of equations in the model which fits the residuals vs the lags (i.e. ′ =).
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There should then be a later stage of analysis to examine whether the errors in the predictions from the regression behave in the same way across the dataset. Thus the question becomes one of the homogeneity of the distribution of the residuals, as the explanatory variables change. See regression analysis.