eteroscedasticità

Heteroscedasticity refers to a situation in statistical modeling, particularly in regression analysis, where the variance of the errors, or residuals, is not constant across all levels of the independent variables. In simpler terms, the spread of the data points around the regression line is not uniform. This is in contrast to homoscedasticity, where the error variance is constant.

The presence of heteroscedasticity can lead to several issues. While the regression coefficients themselves might still be unbiased, their standard errors will be incorrect. This can result in unreliable hypothesis tests and confidence intervals, potentially leading to erroneous conclusions about the significance of predictors. For instance, a variable that appears statistically significant might not be, or vice versa.

Common causes of heteroscedasticity include omitted variables, incorrect functional form of the model, or outliers. It is often observed in cross-sectional data, where observations are taken at a single point in time from different units (e.g., individuals, firms, countries). In time series data, heteroscedasticity can also occur, and specific models like ARCH and GARCH are designed to address it.

Detecting heteroscedasticity can be done through visual inspection of residual plots or using statistical tests such as the Breusch-Pagan test or the White test. If heteroscedasticity is detected, various remedies can be applied. These include transforming the dependent variable (e.g., using logarithms), weighting the observations (using weighted least squares), or employing robust standard errors that are less sensitive to heteroscedasticity.