Forecasting daily river flows using nonlinear time series models

•We use five classes of nonlinear models to analyze Colorado river discharge time series.•We use LS and ML methods to estimate parameters of the models.•We compute three model comparison criteria and ten forecasting performance measures.•The results show that SETAR(3) model perform better than other four competing models.•We use a MC method to build forecasting river discharge confidence intervals.

SummaryIn the hydrology studies, it is well known that the river flows are affected by various factors, and therefore the dynamics in their associated time series are complicated and have nonlinear behaviors. In an empirical study, we investigate the capability of five classes of nonlinear time series models, namely Threshold Autoregressive (TAR), Smooth Transition Autoregressive (STAR), Exponential Autoregressive (EXPAR), Bilinear Model (BL) and Markov Switching Autoregressive (MSAR) to capture the dynamics in the Colorado river discharge time series. Least Squares (LS) and Maximum Likelihood (ML) methods are employed to estimate parameters of the models. For model comparison three criteria, namely loglikelihood, Akaike information criterion (AIC) and Bayesian information criterion (BIC) are calculated. The results show that a self-exciting TAR (SETAR) model performs better than other four competing models. To forecast future river discharge values an iterative method is applied and forecasting confidence intervals are constructed. The out-of-sample 1-day to 5-day ahead forecasting performances of the models based on ten forecast accuracy measures are evaluated. Comparing verification metrics of all models, SETAR model presents the best forecasting performance.