Comparative study of different wavelets for hydrologic forecasting

Use of wavelets in the areas of hydrologic forecasting is increasing in appeal on account of its multi resolution capabilities in addition to its ability to deal with non-stationarities. For successful implementation of wavelets based forecasting methodology, selection of the appropriate mother wavelet form and number of decomposition levels plays an important role. Wavelets based forecasting methodologies have been discussed extensively in published literature but discussion on some key issues of concern such as selection of mother wavelets is rather meager. Appropriately, therefore, this paper presents a comparative evaluation of different wavelet forms when employed for forecasting future states of various kinds of time series. The results suggest that those wavelet forms that have a compact support, for example the Haar wavelet, have a better time localization property and show improved performance in the case of time series that have a short memory with short duration transient features. In contrast, wavelets with wider support, for example db2 and spline wavelets, yielded better forecasting efficiencies in the case of those time series that have long term features. Results further suggest that db2 wavelets perform marginally better as compared to the spline wavelets. It is hoped that this study would enable a reasoned selection of mother wavelets for future forecasting applications.