HarMoTC: Harmonic Temporal Conditioning with Phase–Amplitude Spectral Modeling

Existing time-series forecasting methods primarily model pointwise dependencies in the time domain, making it difficult to preserve both periodic strength and temporal alignment. Moreover, periodic temporal cues are commonly treated only as auxiliary input features. To address these limitations, we propose HarMoTC, a framework that performs temporally conditioned phase–amplitude spectral modeling for multivariate time-series forecasting. HarMoTC explicitly decouples the amplitude and phase of the complex spectrum and employs learnable amplitude rescaling and phase calibration to preserve periodic strength while maintaining temporal alignment. Furthermore, we introduce a conditional spectral modulation mechanism driven by multi-harmonic Fourier encodings of temporal indices, enabling the model to directly modulate spectral transformations according to temporal context and thereby adapt its frequency responses. The resulting architecture jointly captures periodic structure, context-dependent spectral variations, and cross-variable dependencies. Experiments on multiple real-world datasets demonstrate that HarMoTC achieves competitive forecasting performance.