Heteroscedasticity-consistent standard errors
The topic of heteroscedasticity-consistent (HC) standard errors arises in statistics and econometrics in the context of linear regression as well as time series analysis. These are also known as Eicker–Huber–White standard errors (also Huber–White standard errors or White standard errors), to recognize the contributions of Friedhelm Eicker,Peter J. Huber, and Halbert White.
In regression and time-series modelling, basic forms of models make use of the assumption that the errors or disturbances ui have the same variance across all observation points. When this is not the case, the errors are said to be heteroscedastic, or to have heteroscedasticity, and this behaviour will be reflected in the residuals estimated from a fitted model. Heteroscedasticity-consistent standard errors are used to allow the fitting of a model that does contain heteroscedastic residuals. The first such approach was proposed by Huber (1967), and further improved procedures have been produced since for cross-sectional data, time-series data and GARCH estimation.
Assume that we are studying the linear regression model
where X is the vector of explanatory variables and β is a k × 1 column vector of parameters to be estimated.
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