TiF: A Multi‐Scale Data Fusion and Fourier Encoding Framework for Financial Risk Prediction

Financial forecasting often treats annual, quarterly, and monthly information in isolation, which harms robustness in volatile markets. We present Time‐integrated Fourier (TiF), a lightweight framework that fuses annual, quarterly, and monthly signals via energy‐based Fourier encoding and a compact 1D‐CNN backbone with learnable cross‐timescale gating. TiF is evaluated under a standardized rolling‐origin expanding‐window protocol on a core technology benchmark (Apple, Microsoft, Adobe) and further examined on two external validations: (A) a non‐financial EBITDA cohort ( N=105) and (B) a finance‐sector cohort with ROAA as the target. Across studies, some baselines attain the best single‐metric scores (e.g., a Transformer for R2, CatBoost for RMSE), whereas TiF delivers consistently strong and balanced performance over R2/RMSE/MAPE with small variance and modest parameter counts. Ablations quantify the contribution of Fourier bands and each timescale branch, and robustness checks confirm the same qualitative ranking across winsorization/clipping settings. All experiments share identical preprocessing, validation length, and hyperparameter budgets, and we report mean ± SD across rolling origins and seeds to ensure fair comparison.