Time–Frequency Non-Stationary Modeling for Multivariate Time Series Forecasting

Multivariate time series forecasting is important in real-world applications, but practical data often show both temporal and spectral non-stationarity. Existing methods may treat severe spectral drift as informative evolution, allow unreliable spectral components to contaminate temporal representations through credibility-agnostic time--frequency interaction, and infer cross-variable dependencies from noisy local correlations, which may lead to spurious long-term dependencies. To address these issues, we propose TFNS, a dual-stream time--frequency framework for suppressing unreliable spectral evidence under non-stationarity. Specifically, we introduce a Spectral Credibility Estimator to quantify patch-level spectral stability and softly suppress low-credibility frequency components for more reliable frequency modeling; a Credibility-Gated Cross-Interaction module to enable bidirectional time--frequency enhancement while adaptively constraining cross-domain information injection according to spectral reliability; and a Spectral Cointegration Graph to capture stable long-term cross-variable structure in the spectral domain while mitigating spurious dependencies under non-stationary drift. Together, these modules form a progressive pipeline from local spectral purification to reliability-aware cross-domain interaction and robust long-term structure modeling. Experiments on 11 benchmarks show that TFNS achieves state-of-the-art performance, ranking first in 44/55 MSE and 43/55 MAE comparisons.