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Heteroscedasticity often occurs when there is a large difference among the sizes of the observations. A classic example of heteroscedasticity is that of income versus expenditure on meals. A wealthy person may eat inexpensive food sometimes and expensive food at other times. A poor person will almost always eat inexpensive food.
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.
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 modification of one of the tests, they can be found to be algebraically equivalent.
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.
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.
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 ...
In probability theory and statistics, a conditional variance is the variance of a random variable given the value(s) of one or more other variables. Particularly in econometrics, the conditional variance is also known as the scedastic function or skedastic function. [1]
Integrated Generalized Autoregressive Conditional heteroskedasticity (IGARCH) is a restricted version of the GARCH model, where the persistent parameters sum up to one, and imports a unit root in the GARCH process. [9] The condition for this is = + = =.