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.

We also analyze several aspects of our method to demonstrate its advantages.

We also analyze several aspects of our method to demonstrate its advantages.

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.

In this paper we propose an $\ell_1$-regularized GLS estimator for high-dimensional regressions with potentially autocorrelated errors. We establish non-asymptotic oracle inequalities for estimation accuracy in a framework that allows for highly persistent autoregressive errors. In practice, the Whitening matrix required to implement the GLS is unkown, we present a feasible estimator for this matrix, derive consistency results and ultimately show how our proposed feasible GLS can recover closely the optimal performance (as if the errors were a white noise) of the LASSO. A simulation study verifies the performance of the proposed method, demonstrating that the penalized (feasible) GLS-LASSO estimator performs on par with the LASSO in the case of white noise errors, whilst outperforming it in terms of sign-recovery and estimation error when the errors exhibit significant correlation.

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.