Title: PAPer: Periodicity Alignment on Periodic Time Series for Forecasting
Primary area: learning on time series and dynamical systems
Keywords: periodic time series; forecasting

Abstract: Time series forecasting is essential for predicting temporal dynamics across diverse domains, from meteorological patterns to urban traffic flows.
Many such time series exhibit strong periodic patterns, like weekly traffic cycles, and leveraging this periodicity is crucial for forecasting accuracy.
However, existing approaches typically rely on autoregressive models ($x_{t+1} = f(x_t, x_{t-1}, \dots)$) to capture these patterns implicitly or incorporate specialized modules and timestamp embeddings as auxiliary inputs explicitly.
In this work, we propose PAPer: Periodicity Alignment for Periodic Time Series and demonstrate that an explicit yet simple alignment of periodic patterns without auxiliary inputs yields substantial improvements.
We validate PAPer through mathematical proofs, illustrative toy examples, and extensive real-world experiments.
Our results show that PAPer, when applied to state-of-the-art models, achieves performance gains of up to 7\% on multiple benchmarks.
Moreover, PAPer is model-agnostic and can reduce model complexity by up to 99.5\% while incurring only a minor 11\% performance trade-off.
This work presents a foundational investigation into periodicity alignment, and the code is available at xxx.