Wavelet based deseasonalization for modelling and forecasting of daily discharge series considering long range dependence

Short term streamflow forecasting is important for operational control and risk management in hydrology. Despite a wide range of models available, the impact of long range dependence is often neglected when considering short term forecasting. In this paper, the forecasting performance of a new model combining a long range dependent autoregressive fractionally integrated moving average (ARFIMA) model with a wavelet transform used as a method of deseasonalization is examined. It is analysed, whether applying wavelets in order to model the seasonal component in a hydrological time series, is an alternative to moving average deseasonalization in combination with an ARFIMA model. The one-to-ten-steps-ahead forecasting performance of this model is compared with two other models, an ARFIMA model with moving average deseasonalization, and a multiresolution wavelet based model. All models are applied to a time series of mean daily discharge exhibiting long range dependence. For one and two day forecasting horizons, the combined wavelet - ARFIMA approach shows a similar performance as the other models tested. However, for longer forecasting horizons, the wavelet deseasonalization - ARFIMA combination outperforms the other two models. The results show that the wavelets provide an attractive alternative to the moving average deseasonalization.