FreqCast: Frequency-Decoupled Statistical and Deep Learning for Multihorizon Return Forecasting and Price Reconstruction

Abstract

This study forecasts cumulative log returns at horizons of one to twenty trading days and reconstructs future adjusted prices by exponentiating those return forecasts; it does not optimize a price-level loss. This task is difficult because financial returns are nonstationary, heavy-tailed, horizon-dependent, and subject to rapidly changing volatility. We propose FreqCast, which combines a market-conditioned spectral decomposition, a structured state-space branch for the component designated low-frequency, causal multiscale encoders for the components designated intermediate- and high-frequency, and a horizon-conditioned reliability gate. The gate uses expert representations, predictive scale, and cross-expert disagreement to fuse four cumulative-return estimates. The joint objective covers point loss, an auxiliary directional score, Laplace likelihood, ordered quantile loss, decomposition regularization, and horizon coherence. Experiments use eight large U.S. stocks and a single 2021–2024 test interval. Within that restricted benchmark, the reported point estimates favor FreqCast over the included baselines and show horizon- and volatility-dependent expert allocation. Our main contribution is the coordinated frequency-dependent assignment and reliability fusion of heterogeneous forecasting mechanisms, while broad market robustness and statistical superiority remain to be established.