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

Jul 16, 2026

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Time series forecasting demands not only high accuracy but also reasonable forecast volatility across forecast creation dates (FCDs). Even accurate neural models can revise erratically, reducing trust and destabilizing downstream decisions. The work formalizes and promotes a neural architectural design called forking-sequences, which encodes and decodes the full time series across all FCDs in one pass to produce a multi-horizon forecast grid. The approach is analyzed theoretically and empirically using M1, M3, M4, and Tourism datasets, yielding large sCRPS gains and volatility reductions while preserving accuracy.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages43

Reading Time1 h 48 min

Abstract

Introduction

arXiv :2510 .04487v 5 [ cs .LG] 10 Jul 2026 Forking-Sequences: Statistically and Computationally Efficient Multi-Horizon Forecasting with Reduced Volatility Willa Potosnak SCOT Forecasting Science, Amazon Auton Lab, School of Computer Science, Carnegie Mellon University Malcolm Wolff SCOT Forecasting Science, Amazon Mengfei Cao SCOT Forecasting Science, Amazon Ruijun Ma SCOT Forecasting Science, Amazon Tatiana Konstantinova SCOT Forecasting Science, Amazon Dmitry Efimov SCOT Forecasting Science, Amazon Michael W. Mahoney SCOT Forecasting Science, Amazon Boris Oreshkin SCOT Forecasting Science, Amazon Kin G. Olivares SCOT Forecasting Science, Amazon [wpotosna@andrew.cmu.edu](wpotosna@andrew.cmu.edu) [wolfmalc@amazon.com](wolfmalc@amazon.com) [mfcao@amazon.com](mfcao@amazon.com) [ruijunma@amazon.com](ruijunma@amazon.com) [tkonst@amazon.com](tkonst@amazon.com) [defimov@amazon.com](defimov@amazon.com) [zmahmich@amazon.com](zmahmich@amazon.com) [oreshkin@amazon.com](oreshkin@amazon.com) [kigutie@amazon.com](kigutie@amazon.com) Reviewed on OpenReview: [https://openreview.net/forum?id=dXdycy7WCX](https://openreview.net/forum?id=dXdycy7WCX) Abstract 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, stateof-the-art models like MQCNN, MQT, and SPADE employ a powerful yet underexplored neural network architectural design: forking-sequences. This architectural design jointly encodesand 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. Time Series Values 10000 8000 6000 4000 2000 (a) Original Forecasts 1 985-0 1-22 1 985-09-29 1 986-06-06 1 987-02-11 1 987-1 0-19 Time Series Values (b) Forking-sequence Ensembled Forecasts Figure 1: Forecast comparison for a series from the M1 dataset (Makridakis et al., 1982) . (a) Forecasts generated without the forking-sequences ensemble. (b) Forecasts with the forking-sequences ensemble applied. Augmenting the model with the forking-sequences ensemble significantly reduces forecast variability across FCDs, resulting in more stable and consistent forecast distributions. We marked the direction of forecast revisions in red. The lines show P50 (median) forecasts across different FCDs. By reusing encoder computations, forking-sequences enables computationally efficient ensembling with negligible additional computational c

FAQs

What problem does forking-sequences target in multi-horizon forecasting?

It targets excessive forecast volatility across forecast creation dates, where even accurate models can make erratic revisions that undermine trust and operational decisions.

How does forking-sequences differ from conventional neural forecasting approaches?

Forking-sequences jointly encodes and decodes the entire time series across all FCDs to produce a multi-horizon forecast grid in a single forward pass, unlike methods that process each FCD independently.

What benefits does the paper claim and how are they validated?

The paper motivates reduced volatility via ensembling, reduced gradient variance for better statistical efficiency, and improved inference computational efficiency. It validates results against window-sampling on M-series benchmarks using multiple datasets, reporting sCRPS improvements and volatility reductions.

Jul 16, 2026

Upload by Himbo