  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.
