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One of the assumptions of the classical linear regression model is that there is no heteroscedasticity. Breaking this assumption means that the Gauss–Markov theorem does not apply, meaning that OLS estimators are not the Best Linear Unbiased Estimators (BLUE) and their variance is not the lowest of all other unbiased estimators.
In statistics, the Breusch–Pagan test, developed in 1979 by Trevor Breusch and Adrian Pagan, [1] is used to test for heteroskedasticity in a linear regression model. It was independently suggested with some extension by R. Dennis Cook and Sanford Weisberg in 1983 ( Cook–Weisberg test ). [ 2 ]
White test is a statistical test that establishes whether the variance of the errors in a regression model is constant: that is for homoskedasticity. This test, and an estimator for heteroscedasticity-consistent standard errors , were proposed by Halbert White in 1980. [ 1 ]
In regression and time-series modelling, basic forms of models make use of the assumption that the errors or disturbances u i have the same variance across all observation points. When this is not the case, the errors are said to be heteroskedastic, or to have heteroskedasticity , and this behaviour will be reflected in the residuals u ^ i ...
Glejser test for heteroscedasticity, developed in 1969 by Herbert Glejser, is a statistical test, which regresses the residuals on the explanatory variable that is thought to be related to the heteroscedastic variance. [1]
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 ...
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.
A parametric test for equal variance can be visualized by indexing the data by some variable, removing data points in the center and comparing the mean deviations of the left and right side. In statistics, the Goldfeld–Quandt test checks for heteroscedasticity in regression analyses. It does this by dividing a dataset into two parts or groups ...