SFG: A Universal Time-Frequency Architecture for Versatile Time Series Analysis

Time series analysis is essential for finance, transportation, energy, healthcare, and climate research. While time-frequency domain representation underpins effective time series modeling, its holistic utilization and integration with stochastic dynamic modeling remain underexplored. This article proposes SFG, a novel universal time series modeling framework built on the unified Discrete Wavelet Transform (DWT) and Stochastic Differential Equation (SDE) architecture, which fully leverages approximation and detail coefficients of DWT for diverse time series tasks. In the SFG framework, SDE serves as the top-level mathematical backbone, where the DWT-derived low-frequency approximation coefficients are processed by the specialized F Model to learn the deterministic drift term, and the high-frequency detail coefficients are modeled by the dedicated G Model to estimate the stochastic diffusion coefficient, with the reparameterization trick enabling end-to-end trainable fusion. SFG adopts a three-layer architecture: 1) multi-resolution decomposition layer splitting time series into orthogonal approximation and detail coefficients via DWT; 2) dual-branch feature processing layer, where the F-Model extracts stable trend features and the G Model captures dynamic fluctuation patterns; and 3) adaptive fusion mechanism integrating dual-branch outputs via multi-head attention. For enhanced task-specific performance, F-Model outputs serve anomaly detection, and the fused features support classification and forecasting, exploiting the complementary merits of the two coefficients. Extensive experiments show SFG achieves state-of-the-art results on five core time series tasks, outperforming both general-purpose and task-specific baselines. This work advances time-frequency domain analysis and provides a rigorous, lightweight, and edge-deployable framework for integrating spectral information and stochastic dynamic modeling into generic time series modeling.