A Unified Frequency Domain Decomposition Framework for Interpretable and Robust Time Series Forecasting

2025-10-11

AI Summary

Current time-series forecasting models—predominantly black-box deep learning architectures (e.g., linear layers or Transformers)—suffer from poor interpretability and limited adaptability to dynamic distribution shifts across time and frequency domains. To address these limitations, we propose FIRE, a novel interpretable forecasting framework. First, FIRE employs spectral decomposition to decouple amplitude and phase components, modeling them separately. Second, it introduces an adaptive frequency-basis weighting mechanism to enhance robustness against non-stationarity. Third, it designs a joint amplitude-phase optimization objective loss and establishes a new training paradigm tailored for sparse time-series data. Evaluated on multiple long-horizon forecasting benchmarks, FIRE consistently outperforms state-of-the-art methods, achieving simultaneous improvements in both prediction accuracy and model interpretability.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Current approaches for time series forecasting, whether in the time or frequency domain, predominantly use deep learning models based on linear layers or transformers. They often encode time series data in a black-box manner and rely on trial-and-error optimization solely based on forecasting performance, leading to limited interpretability and theoretical understanding. Furthermore, the dynamics in data distribution over time and frequency domains pose a critical challenge to accurate forecasting. We propose FIRE, a unified frequency domain decomposition framework that provides a mathematical abstraction for diverse types of time series, so as to achieve interpretable and robust time series forecasting. FIRE introduces several key innovations: (i) independent modeling of amplitude and phase components, (ii) adaptive learning of weights of frequency basis components, (iii) a targeted loss function, and (iv) a novel training paradigm for sparse data. Extensive experiments demonstrate that FIRE consistently outperforms state-of-the-art models on long-term forecasting benchmarks, achieving superior predictive performance and significantly enhancing interpretability of time series

Problem

• Addressing limited interpretability in time series forecasting models
• Overcoming data distribution dynamics across time and frequency domains
• Providing mathematical abstraction for diverse time series types

Innovation

• Independent amplitude and phase component modeling
• Adaptive learning of frequency basis weights
• Targeted loss function with sparse data training