Beyond Accuracy: A Stability-Aware Metric for Multi-Horizon Forecasting

Traditional time series forecasting methods optimize for accuracy alone. This objective neglects temporal consistency, in other words, how consistently a model predicts the same future event as the forecast origin changes. We introduce the forecast accuracy and coherence score (forecast AC score for short) for measuring the quality of probabilistic multi-horizon forecasts in a way that accounts for both multi-horizon accuracy and stability. Our score additionally provides for user-specified weights to balance accuracy and consistency requirements. As an example application, we implement the score as a differentiable objective function for training seasonal ARIMA models and evaluate it on the M4 Hourly benchmark dataset. Results demonstrate substantial improvements over traditional maximum likelihood estimation. Our AC-optimized models achieve a 75\% reduction in forecast volatility for the same target timestamps while maintaining comparable or improved point forecast accuracy.