Deep probabilistic time series forecasting has gained significant attention due to its superior performance in nonlinear approximation and its ability to provide valuable uncertainty quantification for decision-making tasks. However, many existing models oversimplify the problem by assuming that the error process is time-independent, thereby overlooking the serial correlation in the error process. To overcome this limitation, we propose an innovative training method that incorporates error autocorrelation to further enhance the accuracy of probabilistic forecasting. Our method involves constructing a mini-batch as a collection of $D$ consecutive time series segments for model training and explicitly learning a time-varying covariance matrix over each mini-batch that encodes the 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, and the experimental results confirm the effectiveness of the proposed approach in enhancing the performance of both models across a wide range of datasets, yielding 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卓越性能以及为决策任务提供有价值的不确定性量化能力而受到广泛关注。然而，许多现有模型通过假设误差过程是时间独立的来过度简化问题，从而忽视了误差过程中的序列相关性。为克服这一局限，我们提出一种创新的训练方法，该方法引入误差自相关性以进一步提升概率预测的准确性。我们的方法通过将小批量构建为 $D$ 个连续时间序列片段的集合用于模型训练，并在每个小批量上显式学习一个时变协方差矩阵，该矩阵编码了相邻时间步之间的误差相关性。学习到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及多个公共数据集上评估了该方法，实验结果证实了所提方法在广泛数据集上提升两种模型性能的有效性，并在预测精度上取得了显著改进。