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

> Source: <https://blog.ml.cmu.edu/2026/08/10/forking-sequences-part-ii-multi-horizon-forecast-ensembling-with-reduced-volatility/>
> Published: 2026-08-10 21:52:23+00:00

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 […]