Joint wavelet decomposition of predictors and target variables for drought forecasting

We propose a leakage-free wavelet-based methodology for drought prediction that enables both competitive forecasting performance and improved interpretability of predictor-target relationships. Unlike standard time-series decomposition approaches, the wavelet transform is applied within moving windows of the past values, preventing the use of future information during model training. The method merges local and large-scale climate predictors across multiple temporal scales and is evaluated using 76 years of drought data from Illinois, USA. Predictive performance is assessed using RMSE, SMAPE, MASE, R², and directional accuracy (DA), including uncertainty calculated with seasonal bootstrap confidence intervals. The proposed model frequently outperforms naïve and univariate wavelet baselines, achieving improvements of up to 26.5% in RMSE and 4.95% in SMAPE and higher directional accuracy in diverse scenarios compared to several benchmark methods. Through decomposing both predictors and target variables, the methodology helps characterize how different frequency components are associated with drought evolution, providing a more interpretable representation of hydroclimatic interactions and additional insights into the scale-dependent dynamics of drought processes.