Forecasting High-Frequency River Level Series Using Double Switching Regression with ARMA Errors

River level forecasting is a difficult problem. Complex river dynamics lead to level series with strong time-varying serial correlation and nonlinear relations with influential factors. The current high-frequency level series present a new challenge: they are measured hourly or at finer time scales, but predictions of up to several days ahead are still needed. In this framework, prediction models must be able to provide h-step predictions for high h values. This work presents a new nonlinear model, double switching regression with ARMA errors, that addresses the features of level series. It distinguishes different regimes both in the regression and in the error terms of the model to capture time-varying correlations and nonlinear relations between response and predictors. The use of different regression and ARMA regimes will provide good h-step prediction for both low and high h values. We also propose a new estimation method that, in contrast to other switching models, does not need to define the regimes before estimating the model. This method is based on a two-step estimation and model-based recursive partitioning. The approach is applied to model the hourly levels of the Ebro River in Zaragoza (Spain), using as input an upstream location, Tudela. Using the fitted model, we obtain hourly predictions and confidence intervals up to three days ahead, with very good results. The model outperforms previous approaches, especially with high values and in cases of long-term predictions.