mlsanityData to 14 Oct 2026

Adjusting for Autocorrelated Errors in Neural Networks for Time Series

arXiv 2101.12578 ↗First posted 28 Jan 2021cs.LG stat.MLcited by 18

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Abstract (arXiv)

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.

Key facts. Cited by 18 papers in the map (data through 14 Oct 2026). Builds on 22 of its 85 references that are in the map. First posted on arXiv 28 Jan 2021.

Builds on

22 of 85 references.

References · 22

  1. 2017Attention Is All You Needcited by 60,361
  2. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  3. 2018An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modelingcited by 1,476
  4. 2017DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networkscited by 1,013
  5. 2017Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networkscited by 879
  6. 2019N-BEATS: Neural basis expansion analysis for interpretable time series forecastingcited by 753
  7. 2019Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecastingcited by 607
  8. 2018Deep learning for time series classification: a reviewcited by 576
  9. 2020Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networkscited by 566
  10. 2020Adaptive Graph Convolutional Recurrent Network for Traffic Forecastingcited by 530
  11. 2019Deep Learning for Anomaly Detection: A Surveycited by 358
  12. 2017A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Predictioncited by 245
10 more
  1. 2015Coordinate Descent Algorithmscited by 219
  2. 2017A Multi-Horizon Quantile Recurrent Forecastercited by 211
  3. 2019Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecastingcited by 161
  4. 2019High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processescited by 148
  5. 2020Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flowscited by 144
  6. 2018Temporal Pattern Attention for Multivariate Time Series Forecastingcited by 125
  7. 2018Multivariate LSTM-FCNs for Time Series Classificationcited by 120
  8. 2017Deep Learning for Time-Series Analysiscited by 55
  9. 2013Integrated Pre-Processing for Bayesian Nonlinear System Identification with Gaussian Processescited by 8
  10. 2020Seq2Tens: An Efficient Representation of Sequences by Low-Rank Tensor Projectionscited by 5

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 4; 2023: 4; 2024: 3; 2025: 6; 2026: 1.

18 papers.

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  1. 2022Self-Supervised Contrastive Pre-Training For Time Series via Time-Frequency Consistencycited by 250
  2. 2023SimMTM: A Simple Pre-Training Framework for Masked Time-Series Modelingcited by 115
  3. 2023Nominality Score Conditioned Time Series Anomaly Detection by Point/Sequential Reconstructioncited by 17
  4. 2025PPGF: Probability Pattern-Guided Time Series Forecastingcited by 16
  5. 2024Sub-Adjacent Transformer: Improving Time Series Anomaly Detection with Reconstruction Error from Sub-Adjacent Neighborhoodscited by 10
  6. 2025Deep Learning for Time Series Forecasting: A Surveycited by 10
  7. 2022FreDo: Frequency Domain-based Long-Term Time Series Forecastingcited by 6
  8. 2024Multivariate Probabilistic Time Series Forecasting with Correlated Errorscited by 6
  9. 2023Better Batch for Deep Probabilistic Time Series Forecastingcited by 5
  10. 2023Probabilistic Traffic Forecasting with Dynamic Regressioncited by 4
  11. 2025Simple Feedfoward Neural Networks are Almost All You Need for Time Series Forecastingcited by 2
  12. 2022Optimal Adaptive Prediction Intervals for Electricity Load Forecasting in Distribution Systems via Reinforcement Learningcited by 1
6 more
  1. 2024Link Representation Learning for Probabilistic Travel Time Estimationcited by 1
  2. 2025RINS-T: Robust Implicit Neural Solvers for Time Series Linear Inverse Problemscited by 1
  3. 2022Correlation recurrent units: A novel neural architecture for improving the predictive performance of time-series datacited by 0
  4. 2025Symbol-Temporal Consistency Self-supervised Learning for Robust Time Series Classificationcited by 0
  5. 2025Error Adjustment Based on Spatiotemporal Correlation Fusion for Traffic Forecastingcited by 0
  6. 2026Deep Time-Series Forecasting in 10 Years: A Surveycited by 0