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.
During the last decades several studies in cognitive psychology have shown that many of our actions do not depend on the reasons that we adduce afterwards, when we have to account for them. Our decisions seem to be often influenced by normatively or explanatorily irrelevant features of the environment of which we are not aware, and the reasons we offer for those decisions are a posteriori rationalisations. But exactly what reasons has the psychological research uncovered? In philosophy, a distinction has been commonly made between normative and motivating reasons: normative reasons make an action right, whereas motivating reasons explain our behaviour. Recently, Maria Alvarez has argued that, apart from normative (or justifying) reasons, we should further distinguish between motivating and explanatory reasons. We have, then, three kinds of reasons, and it is not clear which of them have been revealed as the real reasons for our actions by the psychological research. The answer we give to this question will have important implications both for the validity of our classifications of reasons and for our understanding of human action.