A new criteria for determining the best decomposition level and filter for wavelet-based data-driven forecasting frameworks- validating using three case studies on the CAMELS dataset.

Recently, several papers have been published regarding the use of preprocessing models, such as Discrete Wavelet, in Data-Driven Forecasting Frameworks (DDFF). However, these models face unresolved issues, including the use of future data, boundary-affected data, and incorrect selection of decomposition level and wavelet filter, which can lead to inaccurate results. In contrast, the Wavelet-based Data-Driven Forecasting Framework (WDDFF) overcomes these problems. To address the first two issues, we can use Maximal Overlap Discrete Wavelet Transform (MODWT) and a-trous algorithm (AT). Although there is currently no definitive solution for selecting the decomposition level and wavelet filter, we propose a novel approach using Entropy to address these issues. By utilizing the concept of predictability of time series using entropy, we can determine the optimal decomposition level and suitable filter to develop the Maximal Overlap Discrete Wavelet-Entropy Transform (MODWET) and apply it to WDDFF accurately. This study, demonstrates the effectiveness of MODWET through three real-world case studies on the CAMELS data set. In these studies, we will forecast the streamflow of specific stations one month ahead to prove the effectiveness of using preprocessing algorithms for forecasting models. The proposed model combines Input Variable Selection (IVS), preprocessing model, and Data-Driven Model (DDM). We will conclude that MODWET-ANN is the most effective model and highlight how entropy can accurately identify the optimal decomposition level and filter, resolving the concerns associated with using WDDFF in hydrological forecasting problems. [ABSTRACT FROM AUTHOR]