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The Lagrange multiplier (LM) test statistic is the product of the R 2 value and sample size: =. This follows a chi-squared distribution, with degrees of freedom equal to P − 1, where P is the number of estimated parameters (in the auxiliary regression). The logic of the test is as follows.
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.
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.
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.
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.
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 ...
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.