In real-world scenarios, multivariate time series data typically presents a variety of complex characteristics simultaneously, including long-term trends, multiple seasonality, sudden event disturbances and random noise. Owing to remarkable discrepancies among different variables in dimensions, periodic stability and other aspects, and the gradual evolution of these periodic characteristics over time, models are confronted with numerous challenges in handling non-stationarity, multi-scale dynamic variations and heterogeneous fusion of variables. To tackle these problems, this paper proposes a time–frequency parallel fusion framework—TFDG-Net (Time–Frequency Dual-Branch Gated Fusion Network). This framework models the prior information in the frequency domain and the temporal query network in the time domain in parallel, and introduces a channel-wise gating mechanism to achieve more flexible adaptive fusion after data inverse normalization. Such a design enables the model to operate collaboratively on the original physical scale, which not only improves the long-term prediction capability for periodically stable variables, but also effectively suppresses the interference of noise and event-driven factors, thus significantly enhancing prediction accuracy and the robustness of the training process. In multiple long-term prediction benchmark tests covering fields such as energy and finance, compared with various mainstream models, TFDG-Net reduces the mean squared error and mean absolute error by an average of 12.0% and 7.8% respectively.
He et al. (2026) studied this question.