# Neural basis expansion analysis with exogenous variables: Forecasting electricity prices with NBEATSx

arXiv: https://arxiv.org/abs/2104.05522 · HTML: https://mlsanity.com/paper/2104.05522/

## Key facts

- Cited by 64 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 104 references that are in the map.
- First posted on arXiv 12 Apr 2021.

## Builds on (most cited first, 22 of 22)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [Generating Sequences With Recurrent Neural Networks](https://mlsanity.com/paper/1308.0850/) (2013)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [Forecasting day-ahead electricity prices: A review of state-of-the-art algorithms, best practices and an open-access benchmark](https://mlsanity.com/paper/2008.08004/) (2020)
- [Dilated Recurrent Neural Networks](https://mlsanity.com/paper/1710.02224/) (2017)
- [Neural Machine Translation in Linear Time](https://mlsanity.com/paper/1610.10099/) (2016)
- [Transfer learning for time series classification](https://mlsanity.com/paper/1811.01533/) (2018)
- [Unsupervised Pretraining for Sequence to Sequence Learning](https://mlsanity.com/paper/1611.02683/) (2016)
- [STConvS2S: Spatiotemporal Convolutional Sequence to Sequence Network for Weather Forecasting](https://mlsanity.com/paper/1912.00134/) (2019)
- [Forecasting day-ahead electricity prices in Europe: the importance of considering market integration](https://mlsanity.com/paper/1708.07061/) (2017)

## Built on by (most cited first, 30 of 64)

- [Deep Time Series Models: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2407.13278/) (2024)
- [TimeGPT-1](https://mlsanity.com/paper/2310.03589/) (2023)
- [N-HiTS: Neural Hierarchical Interpolation for Time Series Forecasting](https://mlsanity.com/paper/2201.12886/) (2022)
- [SegRNN: Segment Recurrent Neural Network for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2308.11200/) (2023)
- [Aurora: Towards Universal Generative Multimodal Time Series Forecasting](https://mlsanity.com/paper/2509.22295/) (2025)
- [Distributional neural networks for electricity price forecasting](https://mlsanity.com/paper/2207.02832/) (2022)
- [Preformer: Predictive Transformer with Multi-Scale Segment-wise Correlations for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2202.11356/) (2022)
- [CrossLinear: Plug-and-Play Cross-Correlation Embedding for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2505.23116/) (2025)
- [Probabilistic Hierarchical Forecasting with Deep Poisson Mixtures](https://mlsanity.com/paper/2110.13179/) (2021)
- [Deep Generative model with Hierarchical Latent Factors for Time Series Anomaly Detection](https://mlsanity.com/paper/2202.07586/) (2022)
- [FilterTS: Comprehensive Frequency Filtering for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2505.04158/) (2025)
- [Improving Time Series Forecasting via Instance-aware Post-hoc Revision](https://mlsanity.com/paper/2505.23583/) (2025)
- [GCGNet: Graph-Consistent Generative Network for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2603.08032/) (2026)
- [Zero-Shot Time Series Forecasting with Covariates via In-Context Learning](https://mlsanity.com/paper/2506.03128/) (2025)
- [AlphaCast: A Human Wisdom-LLM Intelligence Co-Reasoning Framework for Interactive Time Series Forecasting](https://mlsanity.com/paper/2511.08947/) (2025)
- [HierarchicalForecast: A Reference Framework for Hierarchical Forecasting in Python](https://mlsanity.com/paper/2207.03517/) (2022)
- [Postprocessing of point predictions for probabilistic forecasting of day-ahead electricity prices: The benefits of using isotonic distributional regression](https://mlsanity.com/paper/2404.02270/) (2024)
- [ExoTST: Exogenous-Aware Temporal Sequence Transformer for Time Series Prediction](https://mlsanity.com/paper/2410.12184/) (2024)
- [UniCA: Unified Covariate Adaptation for Time Series Foundation Model](https://mlsanity.com/paper/2506.22039/) (2025)
- [Predicting the Future by Retrieving the Past](https://mlsanity.com/paper/2511.05859/) (2025)
- [A Statistics and Deep Learning Hybrid Method for Multivariate Time Series Forecasting and Mortality Modeling](https://mlsanity.com/paper/2112.08618/) (2021)
- [CoRA: Covariate-Aware Adaptation of Time Series Foundation Models](https://mlsanity.com/paper/2510.12681/) (2025)
- [On-line conformalized neural networks ensembles for probabilistic forecasting of day-ahead electricity prices](https://mlsanity.com/paper/2404.02722/) (2024)
- [Metadata Matters for Time Series: Informative Forecasting with Transformers](https://mlsanity.com/paper/2410.03806/) (2024)
- [CITRAS: Covariate-Informed Transformer for Time Series Forecasting](https://mlsanity.com/paper/2503.24007/) (2025)
- [Dirichlet Proportions Model for Hierarchically Coherent Probabilistic Forecasting](https://mlsanity.com/paper/2204.10414/) (2022)
- [DiffLoad: Uncertainty Quantification in Electrical Load Forecasting with the Diffusion Model](https://mlsanity.com/paper/2306.01001/) (2023)
- [Investigating Compositional Reasoning in Time Series Foundation Models](https://mlsanity.com/paper/2502.06037/) (2025)
- [On the retraining frequency of global models in retail demand forecasting](https://mlsanity.com/paper/2505.00356/) (2025)
- [TFMAdapter: Lightweight Instance-Level Adaptation of Foundation Models for Forecasting with Covariates](https://mlsanity.com/paper/2509.13906/) (2025)

## 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.