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PAMod: Modeling Cyclical Shifts via Phase-Amplitude Modulation for Non-stationary Time Series Forecasting

NeurIPS 2026 · Time series › Causal and generative time series · approach: Probabilistic and conformal forecasting · 0 citations (OpenAlex)

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Proposes PAMod, a lightweight plug-in that models cyclical distribution shifts via learnable phase (mean) and amplitude (variance) embeddings modulating normalized features, evaluated on 12 forecasting benchmarks.

Problem

Non-stationary time series forecasting where RevIN-style normalization assumes identical historical and future distributions, ignoring predictable cyclical mean and variance shifts.

Approach

Learnable cycle-indexed phase (additive mean) and amplitude (multiplicative variance) embeddings modulate features in normalized space, which is argued to be equivalent to dynamic denormalization, unifying distribution adaptation with representation learning.

Key results

• PAMod achieves best MSE/MAE in 7 of 12 datasets' first-place count (19 of 24 MSE/MAE cases best or second best per text), e.g. Traffic MSE 0.434 vs TQNet 0.445 at lookback 96.
• Plugging PAMod into DLinear, PatchTST, iTransformer and TQNet reduces MSE by 2.5%-41.8% on ETTh2 and ETTm1 (e.g. ETTh2 horizon 720 DLinear 0.831 to 0.484).
• PAMod's ETTm1 average MSE is 0.363 vs 0.368 for the second-best TimeEmb in the full table.

Surprising findings

• Modulation in the normalized space is claimed equivalent to dynamic denormalization, and removing the phase term or amplitude term shifts results only modestly on some datasets.

Limitations

• Theoretical guarantee relies on approximate linearity and small-modulation assumptions, and the proof sketch is informal.
• Cycle length must be set per dataset from known periodicity (e.g., via ACF or dataset guidelines), with performance sensitive to mismatched cycle length.

Experimental setup

Datasets: ETTh1 ETTh2 ETTm1 ETTm2 Electricity (ECL) Traffic Solar-Energy Weather PEMS03 PEMS04 PEMS07 PEMS08

Benchmarks: ETTh1 ETTh2 ETTm1 ETTm2 ECL Traffic Solar Weather PEMS03 PEMS04 PEMS07 PEMS08

Metrics: MSE MAE

Baselines: TQNet TimeEmb FilterTS Amplifier TimeXer CycleNet TimeMixer iTransformer PatchTST RevIN SAN DDN

Builds on: RevIN CycleNet TQNet DLinear

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