# Forking-Sequences: Statistically and Computationally Efficient Multi-Horizon Forecasting with Reduced Volatility

arXiv: https://arxiv.org/abs/2510.04487 · HTML: https://mlsanity.com/paper/2510.04487/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 55 references that are in the map.
- First posted on arXiv 6 Oct 2025.

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

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [Semi-supervised Sequence Learning](https://mlsanity.com/paper/1511.01432/) (2015)
- [Learning to Diagnose with LSTM Recurrent Neural Networks](https://mlsanity.com/paper/1511.03677/) (2015)
- [Darts: User-Friendly Modern Machine Learning for Time Series](https://mlsanity.com/paper/2110.03224/) (2021)
- [Dilated Recurrent Neural Networks](https://mlsanity.com/paper/1710.02224/) (2017)
- [MQTransformer: Multi-Horizon Forecasts with Context Dependent and Feedback-Aware Attention](https://mlsanity.com/paper/2009.14799/) (2020)
- [Flexible Model Aggregation for Quantile Regression](https://mlsanity.com/paper/2103.00083/) (2021)
- [Probabilistic Hierarchical Forecasting with Deep Poisson Mixtures](https://mlsanity.com/paper/2110.13179/) (2021)
- [Using dynamic loss weighting to boost improvements in forecast stability](https://mlsanity.com/paper/2409.18267/) (2024)
- [Threshold Martingales and the Evolution of Forecasts](https://mlsanity.com/paper/2105.06834/) (2021)
- [Global Deep Forecasting with Patient-Specific Pharmacokinetics](https://mlsanity.com/paper/2309.13135/) (2023)
- [A More Realistic Evaluation of Cross-Frequency Transfer Learning and Foundation Forecasting Models](https://mlsanity.com/paper/2509.19465/) (2025)

## Built on by (most cited first, 1 of 1)

- [t0: A Time-Series Foundation Model for Forecasting with Context](https://mlsanity.com/paper/2609.24559/) (2026)

## Abstract (arXiv)

While accuracy is a critical requirement for time series forecasting, an equally important desideratum is reasonable forecast volatility across forecast creation dates (FCDs). Even highly accurate models can produce erratic revisions between FCDs, undermining trust and disrupting downstream decision-making. To improve the volatility of forecast revisions, state-of-the-art models like MQCNN, MQT, and SPADE employ a powerful yet underexplored neural network architectural design: forking-sequences. This architectural design jointly encodes and decodes the entire time series across all FCDs, producing an entire multi-horizon forecast grid in a single forward pass. This approach contrasts with conventional neural forecasting methods that process FCDs independently, generating only a single multi-horizon forecast per forward pass. In this work, we formalize the forking-sequences design and motivate its broader adoption by introducing a metric for quantifying excess volatility in forecast revisions and by providing theoretical and empirical analysis. We theoretically motivate three key benefits of forking-sequences: (i) reduced forecast volatility through ensembling; (ii) gradient variance reduction, improving the statistical efficiency of the training procedure; and (iii) improved inference computational efficiency. We validate the benefits of forking-sequences compared to baseline window-sampling on the M-series benchmark, using 16 datasets from the M1, M3, M4, and Tourism competitions. We observe median sCRPS improvements across datasets of 46.2%, 49.3%, 28.6%, 24.7%, and 6.4% for RNN, LSTM, CNN, Transformer, and State Space-based architectures, respectively. We then show that forecast ensembling during inference can reduce median forecast volatility by 13.2%, 13.0%, 10.9%, 10.2%, and 11.2% for these respective models trained with forking-sequences, while maintaining accuracy.