AI & Computational Science

AROpt: An Optimization Method for Autoregressive Time Series Forecasting

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Mathematical optim…Time seriesAutoregressive model

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This paper introduces AROpt, a new training method for time series forecasting that enforces monotonically increasing prediction errors as the forecast horizon extends and enables models to combine short-term autoregressive predictions into longer-term forecasts. The method achieves over 10% reduction in mean squared error compared to state-of-the-art models like iTransformer across multiple benchmark datasets, and allows models trained for short-term forecasting to reliably predict at horizons 7.5 times longer than their original training target.


This approach could significantly improve the accuracy and flexibility of time series forecasting systems used in weather prediction, financial markets, energy grid management, and other domains where reliable long-term predictions are critical. The ability to extend short-horizon models to much longer forecasts without retraining could reduce computational costs and enable more efficient deployment of forecasting systems.


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Mathematical optimization Concept coming soon Time series Concept coming soon Autoregressive model Concept coming soon

⚠️ Preprint – Noch nicht peer-reviewed

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Abstract: Current time-series forecasting models are primarily based on transformer-style neural networks. These models achieve long-term forecasting mainly by scaling up the model size rather than through genuinely autoregressive (AR) rollout. From the perspective of large language model training, traditional time-series forecasting model training ignores the monotonic error-growth heuristic. In this paper, we propose a novel training method for time-series forecasting that enforces two key properties: (1) AR prediction errors should increase with the forecasting horizon. Violations of this trend are interpreted as rollout inconsistency and are softly penalized during training, and (2) the method enables models to be able to concatenate short-term AR predictions to form flexible long-term forecasts. Empirical results demonstrate that our method establishes a new state-of-the-art across multiple benchmarks, achieving an MSE reduction of more than $10%$ compared to iTransformer and other recent strong baselines. Furthermore, it enables short-horizon forecasting models to perform reliable long-term predictions at horizons over 7.5 times longer. Code is available at https://github.com/LizhengMathAi/AROpt

Source: AROpt: An Optimization Method for Autoregressive Time Series Forecasting