Non-parametric time series models for hydrological forecasting

To perform hydrological forecasting, time series methods are often employed. In univariate time series, the autoregressive integrated moving average (ARIMA) model, the seasonal autoregressive moving average (SARMA) model, the deseasonalized model and the periodic autoregressive (PAR) model are often used. These models are based on the assumption that the influence of lagged riverflows on the riverflow is linear. In reality the assumption is often questionable. In this paper, the functional-coefficient autoregression (FCAR) model, which is a nonlinear model, is introduced to forecast riverflows. To explore the influence of the inflow on the outflow in a river system and to exploit the internal interaction of the outflows, bivariate time series models are needed. The transfer function (TF) model and the semi-parametric regression (SPR) model are often employed. In this paper, a new model, the non-parametric and functional-coefficient autoregression (NFCAR) model, is proposed. It consists of two parts: the first part, the non-parametric part explains the influences of the inflows on the outflow in a river system; the second part, the functional-coefficient linear part reveals the interactions among the outflows in a river system. By comparing the calibration and forecasting of the models, it is found that the NFCAR model performs very well.