Deep probabilistic time series forecasting has gained significant attention due to its ability to provide valuable uncertainty quantification for decision-making tasks. However, many existing models oversimplify the problem by assuming the error process is time-independent, thereby overlooking the serial correlation in the error process. This oversight can potentially diminish the accuracy of the forecasts, rendering these models less effective for decision-making purposes. To overcome this limitation, we propose an innovative training method that incorporates error autocorrelation to 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 covariance matrix over each mini-batch that encodes the error correlation among adjacent time steps. The resulting covariance matrix can be used to improve prediction accuracy and enhance uncertainty quantification. We evaluate our method using DeepAR on multiple public datasets, and the experimental results confirm that our framework can effectively capture the error autocorrelation and enhance probabilistic forecasting.

翻译：深度概率时间序列预测因其为决策任务提供有价值的不确定性量化能力而备受关注。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，从而忽略了误差过程中的序列相关性。这种疏忽可能降低预测的准确性，使这些模型在决策目的上效果不佳。为了克服这一局限性，我们提出了一种创新的训练方法，该方法结合误差自相关性以提升概率预测的准确性。我们的方法涉及将小批量构建为$D$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编码相邻时间步长之间误差相关性的协方差矩阵。由此产生的协方差矩阵可用于提高预测精度并增强不确定性量化。我们使用DeepAR在多个公开数据集上评估了我们的方法，实验结果证实，我们的框架能够有效捕捉误差自相关性并提升概率预测性能。