CoRe enhances accuracy and coherence in multivariate time series forecasting
CoRe: Coherence and Relational Alignment for Multivariate Time Series Forecasting
Machine Learning
Summary
Forecasting multiple connected data sequences over time is tricky because predictions often ignore the natural relationships and smooth patterns in the data. The authors propose CoRe, a new way to train forecasting models that focuses on keeping predicted signals both temporally smooth and consistent across variables. Instead of just measuring errors at each point, CoRe uses constraints that maintain the overall shape and relationships in predictions. This approach can be added to many existing forecasting methods and improves their results on common tests.
What this means in practice
- •For financial analysts: Improve forecasting of multiple financial indicators simultaneously to better capture their interdependencies and temporal patterns.
- •For energy demand planners: Generate more coherent and reliable forecasts for multiple energy consumption metrics to optimize supply and grid management.
Authors
Xiaoyu Lin, Huiran Duan, Yining Liu, Zhixiang Wu, Chu Lin, Lin Lu
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.