Forecasting Extremes using Copula Models

Forecasts of extreme events are useful in order to prepare for disaster. Such forecasting can be achieved by existing methods in quantile regression, but these methods cannot capture nonlinearity in the predictors, and cannot capture the distributional tail behaviour. To address these issues, I introduce a method that uses copulas to build nonlinear models, which are fit using the proposed composite nonlinear quantile regression. This new approach is more able to capture the effect that predictors have on a response, and allows for probabilistic forecasts to be issued in the form of the predictive distribution's tail. We end up with a tool that can be used as an early warning system, addressing questions like "how bad could it get?", and is applied to forecast flooding of the Bow River in Alberta.