This CMU ML blog post (Part II of a series) presents forking-sequences as a mechanism for multi-horizon forecast ensembling with reduced volatility. Key contributions include two new forecast volatility metrics — scaled Forecast Percentage Change (sFPC), usable in real-time without ground truth, and scaled Excess Volatility (sEV), which rewards accuracy-improving revisions and only penalizes harmful ones. Empirically, applying exponential-smoothing ensembling (α=0.9) to forking-sequences models reduces sEV by 10–13% across RNN, LSTM, CNN, Transformer, and StateSpace architectures with less than 0.1% accuracy degradation. The technique also works zero-shot on pretrained Time Series Foundation Models (Chronos-2, Toto 2.0, TimesFM, PatchTST, N-BEATS), achieving ~10% volatility reduction at negligible accuracy cost.
Table of contents
Why Forecast Volatility MattersForking-Sequences as a Natural Forecast Ensembling MechanismNew Forecast Volatility MetricsEmpirical Results: Volatility Reduction Without Sacrificing AccuracyA Bonus: Zero-Shot Volatility Reductions for Pretrained Foundation ModelsTakeawaysQuestions this post answers
How much does exponential smoothing ensembling reduce forecast volatility in forking-sequences models without hurting accuracy?
Exponential-smoothing ensembling with α=0.9 reduces scaled Excess Volatility (sEV) by 10.2–13.2% across encoder architectures (RNN, LSTM, CNN, Transformer, StateSpace), with less than 0.1% degradation in sCRPS accuracy. High α weights recent, more accurate forecasts more heavily, giving the best trade-off between volatility reduction and accuracy preservation. Teams evaluating forecasting architectures for production track trade-offs like these on daily.dev.
Can forecast ensembling reduce volatility in pretrained time series foundation models like Chronos or TimesFM without retraining?
Yes. Applying forking-sequences-style forecast ensembling zero-shot to pretrained models — including Chronos-2, Toto 2.0, TimesFM, PatchTST, and N-BEATS — achieves a median ~10% reduction in forecast volatility (sEV) across the M-series benchmark, with less than 0.1% accuracy degradation (sCRPS). No retraining is required; the technique aggregates overlapping forecast revisions at inference time. Practitioners deploying foundation models for forecasting find relevant inference techniques on daily.dev.
What is the difference between sFPC and sEV as forecast volatility metrics?
sFPC (scaled Forecast Percentage Change) measures the relative change in predicted quantiles between consecutive forecast creation dates and can be computed in real time without ground truth. sEV (scaled Excess Volatility) requires ground truth and only penalizes revisions that move forecasts away from the truth or overshoot it, assigning zero penalty to accuracy-improving revisions and full penalty to deteriorating ones. Researchers building forecasting evaluation pipelines discover complementary metrics like these on daily.dev.