Sliding-Window Signatures for Time Series: Application to Electricity Demand Forecasting

2025-10-14

AI Summary

Modeling nonlinear covariate relationships and lagged effects remains challenging in electricity demand forecasting. Method: This paper proposes a ridge regression framework leveraging sliding-window signature features. It avoids manual feature engineering and deep network architectures by employing theoretically grounded signature transforms—endowed with universal approximation capability and stationarity—to automatically encode high-order nonlinear temporal dependencies; an efficient serialization algorithm ensures low-complexity signature computation. Contribution/Results: Experiments on synthetic and real-world electricity load datasets demonstrate that the method significantly outperforms conventional linear models and achieves prediction accuracy comparable to expert-knowledge-driven approaches. The framework offers a novel paradigm for time-series forecasting that is interpretable, lightweight, and theoretically rigorous.

Technology Category

• Machine Learning: Feature Construction/Reformulation
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Computer Vision: Learning & Optimization for CV

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Nonlinear and delayed effects of covariates often render time series forecasting challenging. To this end, we propose a novel forecasting framework based on ridge regression with signature features calculated on sliding windows. These features capture complex temporal dynamics without relying on learned or hand-crafted representations. Focusing on the discrete-time setting, we establish theoretical guarantees, namely universality of approximation and stationarity of signatures. We introduce an efficient sequential algorithm for computing signatures on sliding windows. The method is evaluated on both synthetic and real electricity demand data. Results show that signature features effectively encode temporal and nonlinear dependencies, yielding accurate forecasts competitive with those based on expert knowledge.

Problem

• Capturing nonlinear and delayed covariate effects in time series forecasting
• Developing sliding-window signature features for temporal dynamics encoding
• Improving electricity demand forecasting accuracy without expert knowledge

Innovation

• Sliding-window signature features capture temporal dynamics
• Ridge regression framework enables accurate electricity demand forecasting
• Efficient sequential algorithm computes signatures without expert knowledge