Multivariable time series forecasting methods with exogenous variables enhance prediction accuracy.A novel architecture called Sonnet combines learnable wavelet transformations and spectral analysis for forecasting.Sonnet outperforms competitive baselines on 34 out of 47 forecasting tasks, with an average MAE reduction of 1.1%.Integrating Multivariable Coherence Attention improves forecasting models, reducing MAE by 10.7% on average in challenging tasks.