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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.
Conversely, a “large" R 2 (scaled by the sample size so that it follows the chi-squared distribution) counts against the hypothesis of homoskedasticity. An alternative to the White test is the Breusch–Pagan test, where the Breusch-Pagan test is designed to detect only linear forms of heteroskedasticity. Under certain conditions and a ...
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.
The null hypothesis of this chi-squared test is homoscedasticity, and the alternative hypothesis would indicate heteroscedasticity. Since the Breusch–Pagan test is sensitive to departures from normality or small sample sizes, the Koenker–Bassett or 'generalized Breusch–Pagan' test is commonly used instead.
If the test statistic has a p-value below an appropriate threshold (e.g. p < 0.05) then the null hypothesis of homoskedasticity is rejected and heteroskedasticity assumed. If the Breusch–Pagan test shows that there is conditional heteroskedasticity, one could either use weighted least squares (if the source of heteroskedasticity is known) or ...
Plot with random data showing heteroscedasticity: The variance of the y-values of the dots increases with increasing values of x. In statistics, a sequence of random variables is homoscedastic (/ ˌ h oʊ m oʊ s k ə ˈ d æ s t ɪ k /) if all its random variables have the same finite variance; this is also known as homogeneity of variance ...
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 ...
If, then, in a regression of on the natural logarithm of one or more of the regressors , we arrive at statistical significance for non-zero values on one or more of the ^, we reveal a connection between the residuals and the regressors. We reject the null hypothesis of homoscedasticity and conclude that heteroscedasticity is present.