heteroskedastic

Heteroskedasticity refers to a situation in which the variance of the error terms or the dependent variable is not constant across observations. In regression analysis, it occurs when the spread of the residuals depends on the level of an independent variable or on other characteristics of the data. In cross-sectional data, the variability of the dependent variable may increase with the value of an explanatory variable; in time-series data, volatility may change over time.

Causes of heteroskedasticity include differences in measurement error, omitted variables, subgroups with different variability, sample selection, or structural changes in the data generation process. It is a common feature in economic and social data.

Implications for inference are important. Ordinary least squares (OLS) estimates of coefficients remain unbiased and consistent under heteroskedasticity, but the standard errors are biased. This leads to unreliable hypothesis tests and confidence intervals, even though the coefficient estimates themselves are still informative.

Detection and diagnostics often rely on residual analysis. Tests such as the Breusch-Pagan test, White test, and Goldfeld-Quandt test are commonly used, along with graphical residual plots. In time-series, looking at squared residuals and volatility patterns is informative.

Remedies include using heteroskedasticity-robust standard errors (also called robust or HC1 standard errors) to obtain valid tests. If the form of heteroskedasticity is known, weighted least squares can be appropriate. Transforming the dependent variable (for example, applying a logarithm) can stabilize variance. For time-series data, modeling volatility directly with ARCH or GARCH models or using feasible generalized least squares can address heteroskedasticity.