In many cases, it is difficult to generate highly accurate models for time series data using a known parametric model structure. In response, an increasing body of research focuses on using neural networks to model time series approximately. A common assumption in training neural networks on time series is that the errors at different time steps are uncorrelated. However, due to the temporality of the data, errors are actually autocorrelated in many cases, which makes such maximum likelihood estimation inaccurate. In this paper, we propose to learn the autocorrelation coefficient jointly with the model parameters in order to adjust for autocorrelated errors. For time series regression, large-scale experiments indicate that our method outperforms the Prais-Winsten method, especially when the autocorrelation is strong. Furthermore, we broaden our method to time series forecasting and apply it with various state-of-the-art models. Results across a wide range of real-world datasets show that our method enhances performance in almost all cases.

翻译：在许多情况下,很难用已知的参数模型结构为时间序列数据生成非常精确的模型。 作为回应,越来越多的研究侧重于使用神经网络来模拟时间序列。时间序列培训神经网络的一个共同假设是,不同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,这使得最大可能性估计不准确。在本文中,我们提议与模型参数一起学习自动关系系数,以适应与自动有关的错误。关于时间序列回归,大规模实验表明,我们的方法超过了Prais-Winsten方法,特别是当自动关系强烈时。此外,我们扩大了我们的方法,将时间序列预测扩大到各种最先进的模型中。各种真实世界数据集的结果显示,我们的方法几乎在所有情况下都会提高性能。