An increasing body of research focuses on using neural networks to model time series. A common assumption in training neural networks via maximum likelihood estimation on time series is that the errors across time steps are uncorrelated. However, errors are actually autocorrelated in many cases due to the temporality of the data, which makes such maximum likelihood estimations inaccurate. In this paper, in order to adjust for autocorrelated errors, we propose to learn the autocorrelation coefficient jointly with the model parameters. In our experiments, we verify the effectiveness of our approach on time series forecasting. Results across a wide range of real-world datasets with various state-of-the-art models show that our method enhances performance in almost all cases. Based on these results, we suggest empirical critical values to determine the severity of autocorrelated errors. We also analyze several aspects of our method to demonstrate its advantages. Finally, other time series tasks are also considered to validate that our method is not restricted to only forecasting.

翻译：越来越多的研究侧重于利用神经网络模拟时间序列。通过对时间序列的最大可能性估计来培训神经网络的一个共同假设是,跨时间步骤的错误与时间序列不相干。然而,由于数据的时间性,错误在很多情况下实际上与自动相关,这使得这种最大可能性估计不准确。在本文中,为了适应与自动有关的错误,我们提议与模型参数一起学习自动关系系数。在实验中,我们核查我们的时间序列预测方法的有效性。各种最先进的模型显示,我们的方法几乎在所有情况下都提高了性能。根据这些结果,我们建议了确定与自动化有关的错误严重程度的经验性关键值。我们还分析了我们用来证明其优点的方法的若干方面。最后,还考虑了其他时间序列任务,以证实我们的方法并不限于预测。