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, the traditional training process for time-series forecasting models ignores temporal causality. 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. Any violation of this principle is considered random guessing and is explicitly penalized in the loss function, and (2) the method enables models to concatenate short-term AR predictions for forming 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

翻译：当前的时间序列预测模型主要基于Transformer风格的神经网络。这些模型主要通过扩大模型规模而非真正的自回归（AR）滚动来实现长期预测。从大语言模型训练的角度来看，传统时间序列预测模型的训练过程忽略了时间因果性。本文提出了一种新颖的时间序列预测训练方法，该方法强制实施两个关键特性：（1）自回归预测误差应随预测范围增加而增大。任何违反此原则的情况均被视为随机猜测，并在损失函数中明确惩罚；（2）该方法使模型能够连接短期自回归预测以形成灵活的长期预测。实证结果表明，我们的方法在多个基准测试中确立了新的最优性能，与iTransformer及其他近期强基线相比，均方误差（MSE）降低了超过10%。此外，该方法使短范围预测模型能够在超过7.5倍原范围的更长预测范围内进行可靠的长期预测。代码可在 https://github.com/LizhengMathAi/AROpt 获取。