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In this study, the hybrid wavelet-M5 model was introduced to model the rainfall-runoff process via three different data division strategies (75%–25%, 60%–40%, and 50%–50%) for two different catchments at both daily and monthly scales. The performance of the wavelet-M5 model was also examined in the case of multi-step-ahead forecasting. In this way, first, the rainfall and runoff time series were decomposed using the wavelet transform to several sub-time series to handle the multiresolution characteristic of rainfall and runoff time series. Then the obtained subseries were applied to the M5 model tree as inputs. The obtained results showed the better performance of the wavelet-M5 model in comparison with individual artificial neural network (ANN) and M5 models so that the obtained determination coefficient was 0.80 by the hybrid wavelet-M5 model, while it was calculated as 0.23 and 0.19 by the ANN and M5 tree models, respectively. It was also concluded that the wavelet-M5 model could lead to better performance in the multi-step-ahead forecasting issue since the catchment showed a semilinear behavior because the error would be constant in linear models.
Nourani et al. (2019) studied this question.