Phase aware modulation improves time series forecasting accuracy
Paloma: Phase-Conditioned Residual Modulation for Time Series Forecasting
Machine Learning
Summary
Time series forecasting often separates predictable cycles from leftover data treated as random noise. The authors found that these leftover signals still have patterns linked to different stages of the cycles, which are usually overlooked. They created a method called Paloma that adjusts for these cycle-related changes in direction and size, improving forecast accuracy. Their approach can be added to many existing forecasting tools to boost their performance.
What this means in practice
- •For demand planners: Improve sales and inventory forecasts by integrating phase-aware residual modeling into existing forecasting tools for more accurate seasonality adjustments.
- •For energy grid operators: Enhance load forecasting by incorporating phase-conditioned modulation to better capture periodic deviations in energy consumption data.
Authors
Jingru Fei, Wei Fan, Kun Yi, Qi Zhang, Zhendong Niu
Abstract
Explicitly modeling periodicity has proven to be an efficient approach for time series forecasting, where the residual, obtained after removing the periodic component from the time series, is typically treated as unstructured noise. However, in this work, we show that such residuals still exhibit structured, \textit{phase-dependent} deviations, as supported by both empirical observations and theoretical analysis. This suggests that residuals should not be treated merely as unstructured noise, but instead as \textit{phase-conditioned signals} whose variations arise in both direction and magnitude. Motivated by this perspective and inspired by phase and amplitude modulation in classical signal processing, we propose \textit{Paloma}, a simple yet effective framework for modeling residual deviations. Specifically, Paloma comprises two complementary modules: \textit{a Phase Rotation module}, which performs phase-conditioned rotations to capture directional changes in the feature space, and \textit{an Amplitude Scaling module}, which applies phase-conditioned affine transformations to model magnitude variations. We further abstract the two modules into a general-purpose plugin, termed the \textit{Paloma technique}, which can be readily integrated into existing forecasting architectures to modulate input sequences in a phase-aware manner, enabling backbone models to capture phase-dependent variations in both direction and magnitude. Extensive experiments on twelve datasets demonstrate that Paloma achieves state-of-the-art and robust forecasting performance. Additional results show that the Paloma technique consistently improves a wide range of baseline models, validating its effectiveness as a general-purpose component. Our Code is available at \url{https://github.com/TSTS13/Paloma}.