Traffic Condition Uncertainty Quantification under Nonnormal Distributions

Uncertainty quantification is important for making reliable decisions in transportation planning and operations. In the field of short-term traffic condition forecasting, uncertainty quantification methods include primarily distribution-based approaches and nondistribution-based approaches. For the former, the generalized autoregressive conditional heteroscedasticity (GARCH) model has been widely applied to model and quantify traffic condition uncertainty in terms of prediction interval under normality assumption. However, this normality assumption has not been systematically investigated yet. Therefore, this paper attempts to investigate this normality assumption and thereby quantify traffic condition uncertainty, using a method with steps of residual calculation and investigation, normality investigation, distribution estimation, uncertainty quantification, and performance measurement. Using real-world traffic flow data, the distributions of the selected samples are shown to be nonnormal using the Kolmogorov-Smirnov test and normal probability plot. Distribution estimation using nonnormal models shows that the $t$ location-scale distribution and generalized error distribution (GED) can be used to model traffic condition uncertainty. Uncertainty quantification using GARCH under these nonnormal distributions further show that nonnormal models outperform the normal model, with the GARCH model under $t$ location-scale distribution yielding the best performance. Future studies are recommended to promote the investigation into traffic condition uncertainty quantification and application.