Deep probabilistic time series forecasting has gained attention for its superior performance in nonlinear approximation and its capability to offer valuable uncertainty quantification for decision-making. However, existing models often oversimplify the problem by assuming a time-independent error process, overlooking serial correlation. To overcome this limitation, we propose an innovative training method that incorporates error autocorrelation to enhance probabilistic forecasting accuracy. Our method constructs a mini-batch as a collection of $D$ consecutive time series segments for model training. It explicitly learns a time-varying covariance matrix over each mini-batch, encoding error correlation among adjacent time steps. The learned covariance matrix can be used to improve prediction accuracy and enhance uncertainty quantification. We evaluate our method on two different neural forecasting models and multiple public datasets. Experimental results confirm the effectiveness of the proposed approach in improving the performance of both models across a range of datasets, resulting in notable improvements in predictive accuracy.

翻译：深度概率时间序列预测因其在非线性逼近方面的优异性能以及能为决策提供有价值的不确定性量化而受到关注。然而，现有模型通常通过假设时间无关的误差过程来过度简化问题，从而忽略了序列相关性。为克服这一局限性，我们提出了一种创新的训练方法，该方法整合误差自相关性以提升概率预测的准确性。我们的方法将小批量构建为一组由$D$个连续时间序列片段组成的集合用于模型训练。它显式地学习每个小批量上的时变协方差矩阵，编码相邻时间步之间的误差相关性。所学得的协方差矩阵可用于提高预测精度并增强不确定性量化。我们在两种不同的神经预测模型和多个公开数据集上评估了我们的方法。实验结果证实了所提方法在多个数据集上提升两种模型性能的有效性，并在预测准确性方面带来了显著改进。