CoRe: Coherence and Relational Alignment for Multivariate Time Series Forecasting

2026-09-17

AI Summary

本文提出CoRe，一种用于多变量时间序列预测的模型无关学习目标，通过频谱一致性和低秩关系图约束来改进直接预测方法。

Abstract

Direct forecasting has become a standard paradigm for multivariate time-series forecasting because it predicts the full future horizon in a single pass. However, its training objective is often still decomposed into pointwise errors such as MSE. Such objectives provide stable supervision, but they do not explicitly preserve the structure of the future trajectory: temporal coherence within each variable and relational consistency across variables can both be weakened. We propose CoRe, a model-agnostic learning objective for direct multivariate forecasting. CoRe replaces pointwise supervision with two output-space constraints: a frequency coherence loss that aligns predicted and target spectra, and a low-rank relational graph loss that matches sampled pairwise differences in a target-derived PCA subspace. The resulting objective introduces no trainable parameters and can be applied to existing forecasting backbones by changing only the loss. Experiments on standard benchmarks show that CoRe improves strong baselines, compares favorably with recent forecasting objectives, and remains effective across different backbones, datasets, and hyperparameter settings overall consistently.

Problem

• direct forecasting
• multivariate time series
• temporal coherence
• relational consistency

Innovation

• Coherence
• Relational Alignment
• Multivariate Time Series Forecasting
• Frequency Coherence Loss
• Low-rank Relational Graph Loss