quality:correction, information:extraction
Definition

More generally, if the variance-covariance matrix of disturbance ε i {\displaystyle \varepsilon _{i}} across i {\displaystyle i} has a nonconstant diagonal, the disturbance is heteroscedastic. The matrices below are covariances when there are just three observations across time. The disturbance in matrix A is homoscedastic; this is the simple case where OLS is the best linear unbiased estimator. The disturbances in matrices B and C are heteroscedastic. In matrix B, the variance is time-varying, increasing steadily across time; in matrix C, the variance depends on the value of x {\displaystyle x}. The disturbance in matrix D is homoscedastic because the diagonal variances are constant, even though the off-diagonal covariances are non-zero and ordinary least squares is inefficient for a different reason: serial correlation.