# Deployment-Side Adaptiveness in Multi-Horizon Volatility Forecasting

arXiv: https://arxiv.org/abs/2606.27688 · HTML: https://mlsanity.com/paper/2606.27688/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 31 references that are in the map.
- First posted on arXiv 26 Jun 2026.

## Builds on (most cited first, 10 of 10)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [A Unified Theory of Diversity in Ensemble Learning](https://mlsanity.com/paper/2301.03962/) (2023)
- [Forecast combinations: an over 50-year review](https://mlsanity.com/paper/2205.04216/) (2022)
- [Machine Learning for Financial Forecasting, Planning and Analysis: Recent Developments and Pitfalls](https://mlsanity.com/paper/2107.04851/) (2021)
- [Time-Series Classification for Dynamic Strategies in Multi-Step Forecasting](https://mlsanity.com/paper/2402.08373/) (2024)
- [Epistemic Error Decomposition for Multi-step Time Series Forecasting: Rethinking Bias-Variance in Recursive and Direct Strategies](https://mlsanity.com/paper/2511.11461/) (2025)
- [Expectations vs. Realities: The Cost of MSE-Optimal Forecasting Under Conditional Uncertainty](https://mlsanity.com/paper/2606.04342/) (2026)
- [Exposure Bias as Epistemic Underidentification in Recursive Forecasting](https://mlsanity.com/paper/2606.12990/) (2026)

## Abstract (arXiv)

In financial forecasting, predictive performance depends not only on which model is trained, but also on how the trained model is deployed. We study this issue in multi-horizon volatility forecasting. Our starting point is that a trained multi-output (MIMO) forecaster does not define a single deployable predictor: by changing the inference-time rollout rule, the same trained model induces a family of forecasts with different accuracy and cost profiles. Across 20 stock-volatility series, three forecast horizons, and architectures ranging from linear models to PatchTST, we find that non-default rollout rules often improve over standard MIMO deployment. However, the best fixed rule varies substantially across architectures and horizons, making any single static replacement unreliable. We therefore evaluate validation-based deployment policies over the induced rule family. Under the primary MSE objective, validation-selected singletons provide a low-cost improvement over default MIMO, while small rule subsets recover much of the benefit of larger ensembles at substantially lower inference cost. We also find that policy rankings are metric-sensitive: MSE-selected policies do not transfer uniformly to QLIKE, a finance-standard volatility loss. These results show that inference-time deployment is a meaningful source of adaptiveness in financial forecasting, and that trained volatility forecasters should be evaluated not only by their architecture, but also by their deployment policy.