Patterns Persist, Expressions Change: Long-Horizon Time-Series Forecasting via Temporal Pattern Deformation

Long-horizon forecasting implicitly relies on temporal patterns observed in history remaining informative beyond the observed window. Under structured non-stationarity, recurring patterns may remain informative even as their future expressions change in amplitude, phase, and cross-channel temporal alignment. We term this variation temporal pattern deformation. Existing methods model related phenomena through statistical shifts, spectral variation, latent dynamics, or future phase evolution. We study how recurring temporal structure can be represented together with time-varying amplitude and phase over the forecast horizon. We introduce NSTime, which applies a recursive moving-average decomposition to form a smoothed background and a hierarchy of detail residuals. Each detail residual is represented by an amplitude–phase component and a residual component. Continuous Circular Temporal Generators (CCTG) map historical and forecast time points onto shared differentiable cyclic coordinates, with learned channel offsets representing persistent channel-level temporal shifts. Along these coordinates, the AM–PM Non-Stationary Forecasting (NSF) module evaluates learned amplitude and phase fields over the historical and forecast intervals, while a residual path captures dynamics beyond the amplitude–phase formulation. Across 11 benchmarks, NSTime ranks first in 16 of 22 dataset–metric comparisons within the evaluated comparison pool and among the top two in 19.