StateComp: Shared Transfer of Seasonal States for Compact Forecasting

Long-term time-series forecasting requires preserving fine-grained temporal structure over many future steps, yet learning a fully flexible history-to-future transformation can be parameter-intensive. We explore a complementary hypothesis: time-series shapes may be complex, while the rules governing their evolution can be comparatively simple and shared. Based on this idea, we propose , a compact forecaster that separates the representation of temporal states from their learned transfer. StateComp constructs multi-width seasonal states directly from each input window and propagates them using a small set of coefficients shared across phases and variables. A low-rank history correction complements these prescribed states by capturing residual dependence that seasonal summaries miss. This design allows rich, input-dependent temporal structure to be retained without assigning learned parameters to every phase or variable. We further analyze the interaction between the two components, showing that shared seasonal transfer can represent multiple predictive directions and that correction rank controls the remaining error relative to the coverage of the state dictionary. Across five long-term forecasting benchmarks, StateComp achieves competitive accuracy with only 61–389 learned parameters and obtains lower MSE than SparseTSF and MixLinear at every evaluated horizon on Electricity and Traffic.