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Halo: Improving forecast accuracy through heteroscedastic estimation

arXiv 2609.10589 ↗First posted 6 Sep 2026cs.LGcited by 0

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Abstract (arXiv)

Heteroscedastic forecasting, where a network estimates a scale parameter alongside a location parameter, is normally motivated by uncertainty quantification. This paper shows it also improves the point estimate, in contrast to reported negative results for heteroscedastic estimation outside time series. Halo is a modification that reuses an existing deep forecaster's architecture, giving it a second output for the scale of its implied distribution and training it under the matching negative log likelihood. Adapting three state-of-the-art models --- a transformer, a graph network paired with a variational autoencoder, and a single-layer convolutional network --- under both Gaussian and Laplacian losses demonstrates the phenomenon. On the five electricity price markets of a standard forecasting benchmark, Halo improves MSE and MAE in 28 of 30 model-market-metric comparisons, cutting average MSE by 2.6% to 16.5% and average MAE by 1.7% to 11.0%. Two findings emerge: (1) whether the scale estimate comes from a second projection head or from a full parallel network matters far less than whether the network estimates scale, and (2) the improvement holds under the hyperparameters already tuned for the point-estimate baseline, so retuning is optional.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 19 of its 27 references that are in the map. First posted on arXiv 6 Sep 2026.

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19 of 27 references.

References · 19

  1. 2017Attention Is All You Needcited by 60,361
  2. 2020Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecastingcited by 2,169
  3. 2022A Time Series is Worth 64 Words: Long-term Forecasting with Transformerscited by 2,039
  4. 2021Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecastingcited by 1,676
  5. 2022Are Transformers Effective for Time Series Forecasting?cited by 1,424
  6. 2022FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecastingcited by 1,210
  7. 2017DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networkscited by 1,013
  8. 2017Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networkscited by 879
  9. 2019N-BEATS: Neural basis expansion analysis for interpretable time series forecastingcited by 753
  10. 2022Non-stationary Transformers: Exploring the Stationarity in Time Series Forecastingcited by 391
  11. 2024TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variablescited by 248
  12. 2017A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Predictioncited by 245
7 more
  1. 2017Conditional Time Series Forecasting with Convolutional Neural Networkscited by 123
  2. 2020Forecasting day-ahead electricity prices: A review of state-of-the-art algorithms, best practices and an open-access benchmarkcited by 108
  3. 2022Forecast Evaluation for Data Scientists: Common Pitfalls and Best Practicescited by 55
  4. 2022Faithful Heteroscedastic Regression with Neural Networkscited by 37
  5. 2025DAG: A Dual Correlation Network for Time Series Forecasting with Exogenous Variablescited by 33
  6. 2025CrossLinear: Plug-and-Play Cross-Correlation Embedding for Time Series Forecasting with Exogenous Variablescited by 22
  7. 2026GCGNet: Graph-Consistent Generative Network for Time Series Forecasting with Exogenous Variablescited by 13

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