Beyond Magnitude and Shape: A Direction-Aware Loss for Time Series Forecasting
2026-08-03 • Machine Learning
Machine LearningArtificial Intelligence
AI summaryⓘ
The authors noticed that typical forecasting methods often miss predicting whether values will go up or down, especially for small changes. They created a new way to train models, called CosDir, which focuses on matching the direction of change rather than just the size of the change. Their method can easily be added to existing models and helps improve accuracy in guessing the direction without hurting other predictions. They also made CosDir-UW, which automatically adjusts how much it cares about direction versus size depending on the data. Their extensive tests show better direction predictions across different datasets.
time series forecastingmean squared error (MSE)directional accuracycosine similarityloss functiongradientscale invarianceadaptive weightingplug-in methodfinancial forecasting
Authors
Seunghan Lee, Jaehoon Lee, Jun Seo, Junhyeok Kang, Sangjun Han, Sungdong Yoo, Minjae Kim, Tae Yoon Lim, Dongwan Kang, Hwanil Choi, Soonyoung Lee, Wonbin Ahn
Abstract
The direction of change --- whether a series will move up or down --- is often as important as its exact value in decisiondriven applications such as risk management and financial forecasting. However, most forecasting losses optimize either point magnitude or shape and frequency structure, and none explicitly targets the direction of change. In this paper, we find that MSE-trained forecasters fail on the direction of small moves. To address this, we propose CosDir, a simple yet effective direction-aware loss that aligns the difference vectors of the prediction and the target via cosine similarity. Being scale-invariant, CosDir keeps a directional gradient on small moves, re-injecting learning signal exactly where MSE neglects it. CosDir is a lightweight, plug-in term that attaches to any backbone without architectural modification. Since the best ratio for mixing the directional and magnitude terms differs across datasets, we further propose CosDir-UW, an extension that makes this ratio adaptive by learning it during training, matching a per-dataset tuned weight with no hyperparameter. We conduct over 100K experiments, demonstrating that our method consistently and significantly improves directional accuracy while preserving magnitude accuracy, and that it outperforms various loss functions. Code is available at: https://github.com/seunghan96/cosdir.