FRWKV+: Adaptive Periodic-Position Branch Interaction for Frequency-Space Linear Time Series Forecasting

Long-term time series forecasting is essential for decision making in energy, finance, transportation, and healthcare systems. Recent lightweight forecasting models improve efficiency by operating in transformed or linearized spaces, but two challenges remain in frequency-space forecasting. The real and imaginary streams of complex spectra contain complementary information that is often weakly exchanged, and periodic-position cues can help recurring patterns only when they are reliable for the current dataset and prediction horizon. To address these challenges, we propose FRWKV+, an enhanced FRWKV forecasting model for selective periodic-position branch interaction. FRWKV+ first introduces cross-branch gates that exchange compact contexts between the real and imaginary frequency streams, allowing each stream to modulate the other. It then uses the Adaptive PhaseGate mechanism to extract periodic-position context and generate signed corrections to these gates. An adaptive trust mechanism controls the correction strength at the sample, variable, and channel levels, so periodic-position information is admitted as a reliable correction signal while preserving the efficiency of the FRWKV backbone. External benchmark tables report a separately labeled FRWKV-family selected system for manuscript-level comparison, while mechanism-level claims are based on strict matched-seed FRWKV-family ablations and representative component-level ablations. Under this matched protocol, FRWKV+ achieves the largest MSE winner coverage among the family variants and provides clear gains in selected periodic regimes. Component analysis further supports the usefulness of periodic-position context, signed correction, and adaptive trust in these regimes, while revealing boundary cases where simpler correction rules remain preferable.