← 研踪 PaperTrailarXiv:2611.13228 · v1
Continuous Horizon Forecasting
首次提交 2026-11-10 04:56
版本更新 2026-11-10 04:56
雷达观测 2026-11-11 11:04
摘要
Multi-horizon forecasting has been dominated by discrete forecast strategies that treat model outputs as fixed-vectors or recurrently create them. In this paper, we introduce the Continuous Horizon (CH) strategy that generalizes upon recursive, direct, and multi-step strategies by redefining forecasts as a continuous operator and the forecast horizon as a query variable rather than an index. We present the theoretical foundations for the CH strategy, a Universal Operator Approximation Theorem, and a continuous-horizon bias-variance decomposition that formally proves the estimation variance improvements of CH over the discrete strategies. We validate the CH strategy empirically through a simulation study, and on 16 large-scale datasets from the M-series benchmark, showing how CH achieves competitive RMSE accuracy, while uniquely enabling parallel inference, targeted horizon querying, and interpolation and extrapolation across unseen horizons.
作者备注：International Journal of Forecasting (Work in progress paper)
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v1 · 2026-11-10 04:56 · 最新观测版本
Continuous Horizon Forecasting
Multi-horizon forecasting has been dominated by discrete forecast strategies that treat model outputs as fixed-vectors or recurrently create them. In this paper, we introduce the Continuous Horizon (CH) strategy that generalizes upon recursive, direct, and multi-step strategies by redefining forecasts as a continuous operator and the forecast horizon as a query variable rather than an index. We present the theoretical foundations for the CH strategy, a Universal Operator Approximation Theorem, and a continuous-horizon bias-variance decomposition that formally proves the estimation variance improvements of CH over the discrete strategies. We validate the CH strategy empirically through a simulation study, and on 16 large-scale datasets from the M-series benchmark, showing how CH achieves competitive RMSE accuracy, while uniquely enabling parallel inference, targeted horizon querying, and interpolation and extrapolation across unseen horizons.
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