Neural basis expansion analysis with exogenous variables: Forecasting electricity prices with NBEATSx
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Abstract (arXiv)
We extend the neural basis expansion analysis (NBEATS) to incorporate exogenous factors. The resulting method, called NBEATSx, improves on a well performing deep learning model, extending its capabilities by including exogenous variables and allowing it to integrate multiple sources of useful information. To showcase the utility of the NBEATSx model, we conduct a comprehensive study of its application to electricity price forecasting (EPF) tasks across a broad range of years and markets. We observe state-of-the-art performance, significantly improving the forecast accuracy by nearly 20% over the original NBEATS model, and by up to 5% over other well established statistical and machine learning methods specialized for these tasks. Additionally, the proposed neural network has an interpretable configuration that can structurally decompose time series, visualizing the relative impact of trend and seasonal components and revealing the modeled processes' interactions with exogenous factors. To assist related work we made the code available in https://github.com/cchallu/nbeatsx.
Key facts. Cited by 63 papers in the map (data through 7 Oct 2026). Builds on 22 of its 104 references that are in the map. First posted on arXiv 12 Apr 2021.
Builds on
22 of 104 references.
References · 22
- 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,204
- 2014Adam: A Method for Stochastic Optimizationcited by 36,960
- 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
- 2014Neural Machine Translation by Jointly Learning to Align and Translatecited by 4,530
- 2014Sequence to Sequence Learning with Neural Networkscited by 2,974
- 2014Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modelingcited by 2,341
- 2016WaveNet: A Generative Model for Raw Audiocited by 1,710
- 2018An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modelingcited by 1,447
- 2016On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minimacited by 1,337
- 2014How transferable are features in deep neural networks?cited by 1,216
- 2017DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networkscited by 1,004
- 2019N-BEATS: Neural basis expansion analysis for interpretable time series forecastingcited by 744
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- 2016Language Modeling with Gated Convolutional Networkscited by 688
- 2013Generating Sequences With Recurrent Neural Networkscited by 549
- 2017A Multi-Horizon Quantile Recurrent Forecastercited by 211
- 2020Forecasting day-ahead electricity prices: A review of state-of-the-art algorithms, best practices and an open-access benchmarkcited by 105
- 2017Dilated Recurrent Neural Networkscited by 83
- 2016Neural Machine Translation in Linear Timecited by 65
- 2018Transfer learning for time series classificationcited by 60
- 2016Unsupervised Pretraining for Sequence to Sequence Learningcited by 47
- 2019STConvS2S: Spatiotemporal Convolutional Sequence to Sequence Network for Weather Forecastingcited by 23
- 2017Forecasting day-ahead electricity prices in Europe: the importance of considering market integrationcited by 7
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Citing papers per year: 2021: 4; 2022: 11; 2023: 6; 2024: 8; 2025: 21; 2026: 13.
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