Homoscedasticity and heteroscedasticity

In <a href="/facts/Statistics/DNPsKGYU">statistics</a>, a <a href="/facts/Sequence/gV2S4uqp">sequence</a> of <a href="/facts/Random_variable/TwTBXnLT">random variables</a> is homoscedastic if all its random variables have the same finite <a href="/facts/Variance/ULBJKXD1">variance</a>; this is also known as homogeneity of variance. The complementary notion is called heteroscedasticity, also known as heterogeneity of variance. The spellings homoskedasticity and heteroskedasticity are also frequently used. “Skedasticity” comes from the Ancient Greek word “skedánnymi”, meaning “to scatter”.
Assuming a variable is homoscedastic when in reality it is heteroscedastic (/ˌhɛtəroʊskəˈdæstɪk/) results in <a href="/facts/Biased_estimator/oxIvEgmd">unbiased</a> but <a href="/facts/Efficiency_(statistics)/wTmgEqte">inefficient</a> <a href="/facts/Point_estimate/AYsuptFp">point estimates</a> and in biased estimates of <a href="/facts/Standard_error/Iv96AyCD">standard errors</a>, and may result in overestimating the <a href="/facts/Goodness_of_fit/qlTfUIfS">goodness of fit</a> as measured by the <a href="/facts/Pearson_product-moment_correlation_coefficient/Igf0xDPc">Pearson coefficient</a>.
The existence of heteroscedasticity is a major concern in <a href="/facts/Regression_analysis/n6z5Tf7K">regression analysis</a> and the <a href="/facts/Analysis_of_variance/HHR2jkDk">analysis of variance</a>, as it invalidates <a href="/facts/Statistical_hypothesis_testing/yv9RPF6U">statistical tests of significance</a> that assume that the <a href="/facts/Errors_and_residuals_in_statistics/Ef0LgAS4">modelling errors</a> all have the same variance. While the <a href="/facts/Ordinary_least_squares/q7H9k5vM">ordinary least squares</a> estimator is still unbiased in the presence of heteroscedasticity, it is inefficient and inference based on the assumption of homoskedasticity is misleading. In that case, <a href="/facts/Generalized_least_squares/NI2GL3RK">generalized least squares</a> (GLS) was frequently used in the past. Nowadays, standard practice in econometrics is to include <a href="/facts/Heteroskedasticity-consistent_standard_errors/IrTRLgVp">Heteroskedasticity-consistent standard errors</a> instead of using GLS, as GLS can exhibit strong bias in small samples if the actual <a href="/facts/Skedastic_function/Wh7R7Ype">skedastic function</a> is unknown.
Because heteroscedasticity concerns <a href="/facts/Expected_value/1XV0JKL8">expectations</a> of the second <a href="/facts/Moment_(mathematics)/GL7vJ1nb">moment</a> of the errors, its presence is referred to as <a href="/facts/Statistical_model_specification/d8MInLmL">misspecification</a> of the second order.
The <a href="/facts/Econometrician/7U52gzHt">econometrician</a> <a href="/facts/Robert_Engle/EcBW9M2w">Robert Engle</a> was awarded the 2003 <a href="/facts/Nobel_Memorial_Prize_for_Economics/8BBwNwre">Nobel Memorial Prize for Economics</a> for his studies on <a href="/facts/Regression_analysis/n6z5Tf7K">regression analysis</a> in the presence of heteroscedasticity, which led to his formulation of the <a href="/facts/Autoregressive_conditional_heteroscedasticity/CyPM79ao">autoregressive conditional heteroscedasticity</a> (ARCH) modeling technique.

Homoscedasticity and heteroscedasticity open-in-new

Homoscedasticity and heteroscedasticity