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

Abstract

Recently, numerous papers have been published in the eld of using preprocessing models (e.g. Discrete wavelet) in Data-driven Forecasting Frameworks (DDFF). There are some unresolved problems in these models like using future data, boundary affected data, and miss selection of decomposition level and wavelet lter that cause an erroneous result. However, Wavelet-based Data-driven Forecasting Framework (WDDFF) solves these problems. The rst two problems could be solved using Maximal Overlap Discrete Wavelet Transform (MODWT) and a trous algorithm (AT). As the best we know, there is no absolute solution for decomposition level and wavelet lter selection. Meanwhile, as a novel investigation, we are going to use Entropy to nd a solution for these problems. We are using the concept of predictability of time series using entropy for determining decomposition level and suitable lter, to develop the Maximal Overlap Discrete Wavelet-Entropy Transform (MODWET) to apply in WDDFF correctly. We will reveal the effectiveness of MODWET through three realworld case studies on the CAMELS data set. In these case studies, we will forecast the stream ow of determined stations from one month ahead to prove the effectiveness of using preprocessing models on forecasting accuracy. The proposed model is a combination of Input Variable Selection (IVS), preprocessing model, and Data-Driven Model (DDM). In conclusion, we will show that MODWET-ANN is the best model. In addition, we will realize how good entropy could nd decomposition level and lter, which solves the mentioned concerns about using WDDFF in real-world hydrological forecasting problems.