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.

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