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

Abstract

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.

Keywords

• daily streamflow
• wavelets
• arfima
• deseasonalization
• long range dependence
• forecasting