Dual-Stream Neural Fractional Operator for Nonstationary Multivariate Time Series Forecasting

Ruizhe Zheng, HAO SHEN, Chendrayan Dineshkumar, Yuguo Yu

Keywords: time series forecasting, dynamical system

TL;DR: A new long-term time series forecasting model inspired by fractional operator.

Abstract: Long-term, multivariate time‑series forecasting is vital for domains such as energy systems, finance, and weather prediction, where accurately modeling intricate patterns can yield significant performance gains. However, many existing models struggle with the inherent non‑stationarity of real‑world data—distribution shifts can vary both within and across series—leading to suboptimal long‑horizon forecasts. While techniques like normalization and decomposition have been applied to learn more nuanced features, they often rely on restrictive assumptions. To overcome these limitations, we propose a dual-stream system is built on stacked neural fractional operators, each performing fractional‑domain, time‑varying transformations with interwoven decomposition to extract non‑stationary sub-components for weaving the target signals. By producing a hierarchy of sub‑forecasts that are progressively aggregated, our model effectively captures both intra‑series and inter‑series dependencies in a non‑stationarity‑aware manner. Extensive experiments show that our approach achieves state‑of‑the‑art (SOTA) performance, surpassing recent decomposition-based and transformed domain models, further validating its robustness and effectiveness.

Primary Area: learning on time series and dynamical systems

Submission Number: 4957