A Comparison of Nonlinear Stochastic Self-Exciting Threshold Autoregressive and Chaotic <Emphasis Type="Italic">k</Emphasis>-Nearest Neighbour Models in Daily Streamflow Forecasting

A nonlinear stochastic self-exciting threshold autoregressive (SETAR) model and a chaotic k-nearest neighbour (k-nn) model, for the first time, were compared in one and multi-step ahead daily flow forecasting for nine rivers with low, medium, and high flows in the western United States. The embedding dimension and the number of nearest neighbours of the k-nn model and the parameters of the SETAR model were identified by a trial-and-error process and a least mean square error estimation method, respectively. Employing the recursive forecasting strategy for the first time in multi-step forecasting of SETAR and k-nn, the results indicated that SETAR is superior to k-nn by means of performance indices. SETAR models were found to be more efficient in forecasting flows in one and multi-step forecasting. SETAR is less sensitive to the propagated error variances than the k-nn model, particularly for larger lead times (i.e., 5 days). The k-nn model should carefully be used in multi-step ahead forecasting where peak flow forecasting is important by considering the risk of error propagation.