To See Far, Look Close: Evolutionary Forecasting for Long-term Time Series

TL;DR

This paper challenges the conventional Direct Forecasting paradigm for long-term time series forecasting by decoupling the model’s output horizon from the evaluation horizon. It introduces Evolutionary Forecasting (EF), a block-wise, generative framework where a single model produces $L$-length Reasoning Blocks that concatenate to form the target horizon $H$, with $K=\lceil H/L\rceil$. The authors prove that DF is a degenerate case of EF and demonstrate, through extensive experiments across diverse real-world datasets, that EF consistently outperforms horizon-specific DF ensembles, even in extreme extrapolation where errors typically accumulate. They also diagnose an optimization pathology in DF—gradient conflicts across near-term and distal horizons—that EF mitigates, enabling robust, scalable long-horizon forecasting. Overall, the work advocates moving from static horizon mappings to autonomous evolutionary reasoning for time series forecasting, with strong implications for efficiency and generalization in practice.

Abstract

The prevailing Direct Forecasting (DF) paradigm dominates Long-term Time Series Forecasting (LTSF) by forcing models to predict the entire future horizon in a single forward pass. While efficient, this rigid coupling of output and evaluation horizons necessitates computationally prohibitive re-training for every target horizon. In this work, we uncover a counter-intuitive optimization anomaly: models trained on short horizons-when coupled with our proposed Evolutionary Forecasting (EF) paradigm-significantly outperform those trained directly on long horizons. We attribute this success to the mitigation of a fundamental optimization pathology inherent in DF, where conflicting gradients from distant futures cripple the learning of local dynamics. We establish EF as a unified generative framework, proving that DF is merely a degenerate special case of EF. Extensive experiments demonstrate that a singular EF model surpasses task-specific DF ensembles across standard benchmarks and exhibits robust asymptotic stability in extreme extrapolation. This work propels a paradigm shift in LTSF: moving from passive Static Mapping to autonomous Evolutionary Reasoning.

Figures (9)

• Figure 1: MSE comparison of $96$-horizon forecasting on common real-world datasets. Using a fixed input length $T=720$, we compare models trained directly with an output horizon $L$ matching the evaluation horizon ($L=96$, solid bars) against models trained with a longer output horizon ($L=720$, hatched bars). For the latter, predictions are obtained by truncating the long series to match $96$. Lower bars indicate better performance. The results demonstrate that truncation leads to sub-optimal performance compared to directly training for the target horizon.
• Figure 2: The workflow and shortcoming of Direct Forecasting.
• Figure 3: The workflow of Evolutionary Forecasting. Blue items are historical observation.
• Figure 4: Statistical Dominance in the EF Paradigm. LEFT: We report the Win Ratio into the EF paradigm between the non-DF ($L \neq H$, red line) cases versus the conventional DF paradigm ($L=H$, blue line) across various input lengths $T$. The gray bars represent the marginal probability distribution of optimal performance relative to the input length $T$. RIGHT: We select the set of best input-output parameters $T^*,L*$ where each model perform as best as possible under the EF paradigm on all evaluation horizon. The win ratio is calculated between the DF with the same input length ($T^*$) and the DF with input length that perform best inside the DF paradigm.
• Figure 5: LEFT: Visualization of Gradient Conflict and Distal Dominance in DF paradigm on $T=L=720$. We compute the average cosine similarity of gradients across partitioned forecasting segments ($[1, 96]$ to $(336, 720]$) and the total sequence ("All") during training. RIGHT: Extreme LTSF on $T=720$.

Theorems & Definitions (3)

• Definition 4.1
• Definition 4.2
• Remark 4.3