Comparative analysis of three recursive real-time river flow forecasting models: deterministic, stochastic, and coupled deterministic-stochastic

The objective of the paper is to compare three recursive linear state space models used to forecast river flow. The three models are as follows: (i) Purely deterministic discrete linear cascade model (DLCM); (ii) Purely stochastic autoregressive moving average (ARMAX) time series model; and (iii) Coupled deterministic (DLCM) — stochastic (ARMA) model. Description of DLCM is given shortly. The state space formulation of the ARMAX model enables the recursive estimation of random walk parameters and the forecast of flows by linear Kalman filtering. The correlated error sequence of DLCM is described by an ARMA model. The DLCM and ARMA models are put together in a coupled deterministic-stochastic model. The recursive conditional forecasting of the augmented state vector is performed by the linear Kalman-filter. The conditional output forecast is given by linear projection of thea priori state vector. Numerical investigations on River Danube data lead to the conclusion that the coupled deterministic-stochastic model is the most efficient forecasting model of all the three recursive techniques compared.