Adaptive Oscillatory-State Alignment for Time Series Forecasting

2026-06-04

AI Summary

Traditional periodic modeling approaches rely on fixed templates, which struggle to capture nonstationary dynamics such as amplitude modulation, phase drift, and local frequency variations, leading to mismatches with real oscillatory states. This work proposes AOSNET, a framework that leverages the Hilbert transform to extract analytic signal descriptors and introduces a learnable global oscillation prior coupled with a descriptor-conditioned gating mechanism to enable adaptive alignment between observed sequences and local oscillatory states. By reframing periodic forecasting from static template matching to dynamic oscillation referencing, AOSNET substantially enhances modeling capacity for complex nonstationary time series. Evaluated on eight benchmark datasets, the method achieves state-of-the-art or highly competitive prediction accuracy with efficient inference; synthetic experiments further confirm its superiority in scenarios with intensified nonstationarity.

Abstract

Long-term time series forecasting benefits from inductive biases that expose recurring temporal structure. Existing periodic forecasting methods typically model recurrence through predefined periods, global spectral components, or fixed learnable templates. However, real-world temporal dynamics are rarely rigidly periodic: oscillatory behavior often evolves through amplitude modulation, phase drift, and local frequency variation. Under these conditions, fixed-template periodic modeling can become fundamentally mismatched to the underlying temporal states. We propose AOSNET, a Hilbert-guided forecasting framework that reformulates periodic forecasting from fixed template matching to adaptive oscillatory-state alignment. AOSNET extracts analytic-signal descriptors from both the observed sequence and a learnable global oscillatory prior, then adaptively aligns local states through a descriptor-conditioned gate that selectively preserves reliable observations while softly correcting mismatched regions. The learned prior serves not as a rigid repeated template but as a flexible oscillatory reference interpreted through local state dynamics. Experiments on eight benchmarks demonstrate state-of-the-art or highly competitive accuracy with fast inference speed. Controlled synthetic studies isolating amplitude modulation, phase drift, and local frequency variation confirm that the advantage of oscillatory-state alignment consistently increases as non-stationarity intensifies.

Problem

• time series forecasting
• non-stationary periodicity
• oscillatory dynamics
• phase drift
• amplitude modulation

Innovation

• adaptive oscillatory-state alignment
• analytic signal
• Hilbert transform
• non-stationary time series
• learnable oscillatory prior