Comparing Prediction Intervals in Quantile and OLS Regression

In the regression framework, prediction intervals are a valuable tool to estimate the value of the response variable. Such prediction intervals can be formulated in terms of the expected value of the response variable as well as for a single specific value. Both the type of intervals suffer of violations of the assumptions of the classical regression models, resulting in empirical coverage levels not consistent with the nominal levels. Among the several possibilities proposed in literature to face this problem, we consider the estimations provided by quantile regression at two different quantiles to obtain prediction intervals. Exploiting the non parametric nature of quantile regression, such intervals are useful in situations characterised by heteroscedasticity or when the response variable is skewed.