Confidence Bands for ROC Curves with Serially Dependent Data

Abstract

We propose serial correlation-robust asymptotic confidence bands for the receiver operating characteristic (ROC) curve and its functional, viz. the area under ROC curve (AUC), estimated by quasi-maximum likelihood in the binormal model. Our simulation experiments confirm that this new method performs fairly well in finite samples, and confers an additional measure of robustness to non-normality. The conventional procedure is found to be markedly undersized in terms of yielding empirical coverage probabilities lower than the nominal level, especially when the serial correlation is strong. An example from macroeconomic forecasting demonstrates the importance of accounting for serial correlation when the probability forecasts for real GDP declines are evaluated using ROC.

Keywords: Receiver operating characteristic curve, AUC, Binormal model, Quasi-maximum likelihood, Serial correlation, Survey of Professional Forecasters, Robustness to skewness and excess kurtosis

JEL Classification: C01, C12, C13, C15, C22, C25, C51, C53, E17, E37