Under adversarial attacks, time series regression and classification are vulnerable. Adversarial defense, on the other hand, can make the models more resilient. It is important to evaluate how vulnerable different time series models are to attacks and how well they recover using defense. The sensitivity to various attacks and the robustness using the defense of several time series models are investigated in this study. Experiments are run on seven time series models with three adversarial attacks and one adversarial defense. According to the findings, all models, particularly GRU and RNN, appear to be vulnerable. LSTM and GRU also have better defense recovery. FGSM exceeds the competitors in terms of attacks. PGD attacks are more difficult to recover from than other sorts of attacks.

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.