Forking-Sequences — Part II: Multi-Horizon Forecast Ensembling with Reduced Volatility

Researchers from the University of California, Berkeley, Amazon, and other institutions introduced forking-sequences, a method that generates overlapping forecasts for every target date in a single forward pass, enabling forecast ensembling at inference with no extra encoder computation. Applying exponential-smoothing ensembling (α = 0.9) to pretrained time series foundation models including Chronos-2, Toto 2.0, TimesFM, PatchTST, and N-BEATS reduced forecast volatility by approximately 10% with less than 0.1% accuracy degradation, as detailed in a paper published in Transactions on Machine Learning Research in 2026.

Based on: Potosnak, W., Wolff, M., Cao, M., Ma, R., Konstantinova, T., Efimov, D., Mahoney, M.W., Oreshkin, B., & Olivares, K.G. "Forking-Sequences: Statistically and Computationally Efficient Multi-Horizon Forecasting with Reduced Volatility." Transactions on Machine Learning Research, 2026. Disclaimer: Code implementation not used in the paper; not affiliated with Amazon — provided as a reference for forking-sequences and forecast ensembling TL;DR Ensembling, nearly for free. Forking-sequences already produces overlapping forecasts for every target date across FCDs in a single forward pass, so ensembling them at inference adds no extra encoder computation compared with window-sampling. Two new forecast volatility metrics. scaled Forecast Percentage Change sFPC measures raw revision size in real time no ground truth needed ; Excess Volatility EV goes further, rewarding accuracy-improving revisions and only penalizing the ones that move forecasts away from the truth or overshoot it. Reduced volatility without sacrificing accuracy. Exponential-smoothing forecast ensembling α = 0.9 reduces sEV by 10–13% across all encoder types, with less than 0.1% accuracy degradation. Works zero-shot on models pretrained with window-sampling. Forecast ensembling applied to pretrained Time Series Foundation Models TSFMs — Chronos-2, Toto 2.0, TimesFM, PatchTST, N-BEATS — cuts volatility by ~10% with negligible accuracy cost less than 0.1% . In Part …